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Simplifying 5(x + 4) + -1x(2x + -3) = 0 Reorder the terms: 5(4 + x) + -1x(2x + -3) = 0 (4 * 5 + x * 5) + -1x(2x + -3) = 0 (20 + 5x) + -1x(2x + -3) = 0 Reorder the terms: 20 + 5x + -1x(-3 + 2x) = 0 20 + 5x + (-3 * -1x + 2x * -1x) = 0 20 + 5x + (3x + -2x2) = 0 Combine like terms: 5x + 3x = 8x 20 + 8x + -2x2 = 0 Solving 20 + 8x + -2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(10 + 4x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(10 + 4x + -1x2)' equal to zero and attempt to solve: Simplifying 10 + 4x + -1x2 = 0 Solving 10 + 4x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -10 + -4x + x2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + -4x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + -4x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -4x + x2 = 0 + 10 -4x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 -4x + x2 = 10 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 10 + 4 Reorder the terms: 4 + -4x + x2 = 10 + 4 Combine like terms: 10 + 4 = 14 4 + -4x + x2 = 14 Factor a perfect square on the left side: (x + -2)(x + -2) = 14 Calculate the square root of the right side: 3.741657387 Break this problem into two subproblems by setting (x + -2) equal to 3.741657387 and -3.741657387.Subproblem 1
x + -2 = 3.741657387 Simplifying x + -2 = 3.741657387 Reorder the terms: -2 + x = 3.741657387 Solving -2 + x = 3.741657387 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 3.741657387 + 2 Combine like terms: -2 + 2 = 0 0 + x = 3.741657387 + 2 x = 3.741657387 + 2 Combine like terms: 3.741657387 + 2 = 5.741657387 x = 5.741657387 Simplifying x = 5.741657387Subproblem 2
x + -2 = -3.741657387 Simplifying x + -2 = -3.741657387 Reorder the terms: -2 + x = -3.741657387 Solving -2 + x = -3.741657387 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -3.741657387 + 2 Combine like terms: -2 + 2 = 0 0 + x = -3.741657387 + 2 x = -3.741657387 + 2 Combine like terms: -3.741657387 + 2 = -1.741657387 x = -1.741657387 Simplifying x = -1.741657387Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.741657387, -1.741657387}Solution
x = {5.741657387, -1.741657387}
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