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Simplifying 5(4x + 6) + -2(x + -4) = 7x(x + -2) + -48 Reorder the terms: 5(6 + 4x) + -2(x + -4) = 7x(x + -2) + -48 (6 * 5 + 4x * 5) + -2(x + -4) = 7x(x + -2) + -48 (30 + 20x) + -2(x + -4) = 7x(x + -2) + -48 Reorder the terms: 30 + 20x + -2(-4 + x) = 7x(x + -2) + -48 30 + 20x + (-4 * -2 + x * -2) = 7x(x + -2) + -48 30 + 20x + (8 + -2x) = 7x(x + -2) + -48 Reorder the terms: 30 + 8 + 20x + -2x = 7x(x + -2) + -48 Combine like terms: 30 + 8 = 38 38 + 20x + -2x = 7x(x + -2) + -48 Combine like terms: 20x + -2x = 18x 38 + 18x = 7x(x + -2) + -48 Reorder the terms: 38 + 18x = 7x(-2 + x) + -48 38 + 18x = (-2 * 7x + x * 7x) + -48 38 + 18x = (-14x + 7x2) + -48 Reorder the terms: 38 + 18x = -48 + -14x + 7x2 Solving 38 + 18x = -48 + -14x + 7x2 Solving for variable 'x'. Reorder the terms: 38 + 48 + 18x + 14x + -7x2 = -48 + -14x + 7x2 + 48 + 14x + -7x2 Combine like terms: 38 + 48 = 86 86 + 18x + 14x + -7x2 = -48 + -14x + 7x2 + 48 + 14x + -7x2 Combine like terms: 18x + 14x = 32x 86 + 32x + -7x2 = -48 + -14x + 7x2 + 48 + 14x + -7x2 Reorder the terms: 86 + 32x + -7x2 = -48 + 48 + -14x + 14x + 7x2 + -7x2 Combine like terms: -48 + 48 = 0 86 + 32x + -7x2 = 0 + -14x + 14x + 7x2 + -7x2 86 + 32x + -7x2 = -14x + 14x + 7x2 + -7x2 Combine like terms: -14x + 14x = 0 86 + 32x + -7x2 = 0 + 7x2 + -7x2 86 + 32x + -7x2 = 7x2 + -7x2 Combine like terms: 7x2 + -7x2 = 0 86 + 32x + -7x2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -12.28571429 + -4.571428571x + x2 = 0 Move the constant term to the right: Add '12.28571429' to each side of the equation. -12.28571429 + -4.571428571x + 12.28571429 + x2 = 0 + 12.28571429 Reorder the terms: -12.28571429 + 12.28571429 + -4.571428571x + x2 = 0 + 12.28571429 Combine like terms: -12.28571429 + 12.28571429 = 0.00000000 0.00000000 + -4.571428571x + x2 = 0 + 12.28571429 -4.571428571x + x2 = 0 + 12.28571429 Combine like terms: 0 + 12.28571429 = 12.28571429 -4.571428571x + x2 = 12.28571429 The x term is -4.571428571x. Take half its coefficient (-2.285714286). Square it (5.224489797) and add it to both sides. Add '5.224489797' to each side of the equation. -4.571428571x + 5.224489797 + x2 = 12.28571429 + 5.224489797 Reorder the terms: 5.224489797 + -4.571428571x + x2 = 12.28571429 + 5.224489797 Combine like terms: 12.28571429 + 5.224489797 = 17.510204087 5.224489797 + -4.571428571x + x2 = 17.510204087 Factor a perfect square on the left side: (x + -2.285714286)(x + -2.285714286) = 17.510204087 Calculate the square root of the right side: 4.184519577 Break this problem into two subproblems by setting (x + -2.285714286) equal to 4.184519577 and -4.184519577.Subproblem 1
x + -2.285714286 = 4.184519577 Simplifying x + -2.285714286 = 4.184519577 Reorder the terms: -2.285714286 + x = 4.184519577 Solving -2.285714286 + x = 4.184519577 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.285714286' to each side of the equation. -2.285714286 + 2.285714286 + x = 4.184519577 + 2.285714286 Combine like terms: -2.285714286 + 2.285714286 = 0.000000000 0.000000000 + x = 4.184519577 + 2.285714286 x = 4.184519577 + 2.285714286 Combine like terms: 4.184519577 + 2.285714286 = 6.470233863 x = 6.470233863 Simplifying x = 6.470233863Subproblem 2
x + -2.285714286 = -4.184519577 Simplifying x + -2.285714286 = -4.184519577 Reorder the terms: -2.285714286 + x = -4.184519577 Solving -2.285714286 + x = -4.184519577 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.285714286' to each side of the equation. -2.285714286 + 2.285714286 + x = -4.184519577 + 2.285714286 Combine like terms: -2.285714286 + 2.285714286 = 0.000000000 0.000000000 + x = -4.184519577 + 2.285714286 x = -4.184519577 + 2.285714286 Combine like terms: -4.184519577 + 2.285714286 = -1.898805291 x = -1.898805291 Simplifying x = -1.898805291Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.470233863, -1.898805291}
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