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Simplifying 2x(x + -4) = x + 7 Reorder the terms: 2x(-4 + x) = x + 7 (-4 * 2x + x * 2x) = x + 7 (-8x + 2x2) = x + 7 Reorder the terms: -8x + 2x2 = 7 + x Solving -8x + 2x2 = 7 + x Solving for variable 'x'. Reorder the terms: -7 + -8x + -1x + 2x2 = 7 + x + -7 + -1x Combine like terms: -8x + -1x = -9x -7 + -9x + 2x2 = 7 + x + -7 + -1x Reorder the terms: -7 + -9x + 2x2 = 7 + -7 + x + -1x Combine like terms: 7 + -7 = 0 -7 + -9x + 2x2 = 0 + x + -1x -7 + -9x + 2x2 = x + -1x Combine like terms: x + -1x = 0 -7 + -9x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3.5 + -4.5x + x2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + -4.5x + 3.5 + x2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + -4.5x + x2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + -4.5x + x2 = 0 + 3.5 -4.5x + x2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 -4.5x + x2 = 3.5 The x term is -4.5x. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5x + 5.0625 + x2 = 3.5 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = 3.5 + 5.0625 Combine like terms: 3.5 + 5.0625 = 8.5625 5.0625 + -4.5x + x2 = 8.5625 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = 8.5625 Calculate the square root of the right side: 2.926174978 Break this problem into two subproblems by setting (x + -2.25) equal to 2.926174978 and -2.926174978.Subproblem 1
x + -2.25 = 2.926174978 Simplifying x + -2.25 = 2.926174978 Reorder the terms: -2.25 + x = 2.926174978 Solving -2.25 + x = 2.926174978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = 2.926174978 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 2.926174978 + 2.25 x = 2.926174978 + 2.25 Combine like terms: 2.926174978 + 2.25 = 5.176174978 x = 5.176174978 Simplifying x = 5.176174978Subproblem 2
x + -2.25 = -2.926174978 Simplifying x + -2.25 = -2.926174978 Reorder the terms: -2.25 + x = -2.926174978 Solving -2.25 + x = -2.926174978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = -2.926174978 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -2.926174978 + 2.25 x = -2.926174978 + 2.25 Combine like terms: -2.926174978 + 2.25 = -0.676174978 x = -0.676174978 Simplifying x = -0.676174978Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.176174978, -0.676174978}
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