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Simplifying 90(x + 4) + 15(x) = 4x(x + 4) Reorder the terms: 90(4 + x) + 15(x) = 4x(x + 4) (4 * 90 + x * 90) + 15(x) = 4x(x + 4) (360 + 90x) + 15(x) = 4x(x + 4) Combine like terms: 90x + 15x = 105x 360 + 105x = 4x(x + 4) Reorder the terms: 360 + 105x = 4x(4 + x) 360 + 105x = (4 * 4x + x * 4x) 360 + 105x = (16x + 4x2) Solving 360 + 105x = 16x + 4x2 Solving for variable 'x'. Combine like terms: 105x + -16x = 89x 360 + 89x + -4x2 = 16x + 4x2 + -16x + -4x2 Reorder the terms: 360 + 89x + -4x2 = 16x + -16x + 4x2 + -4x2 Combine like terms: 16x + -16x = 0 360 + 89x + -4x2 = 0 + 4x2 + -4x2 360 + 89x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 360 + 89x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -90 + -22.25x + x2 = 0 Move the constant term to the right: Add '90' to each side of the equation. -90 + -22.25x + 90 + x2 = 0 + 90 Reorder the terms: -90 + 90 + -22.25x + x2 = 0 + 90 Combine like terms: -90 + 90 = 0 0 + -22.25x + x2 = 0 + 90 -22.25x + x2 = 0 + 90 Combine like terms: 0 + 90 = 90 -22.25x + x2 = 90 The x term is -22.25x. Take half its coefficient (-11.125). Square it (123.765625) and add it to both sides. Add '123.765625' to each side of the equation. -22.25x + 123.765625 + x2 = 90 + 123.765625 Reorder the terms: 123.765625 + -22.25x + x2 = 90 + 123.765625 Combine like terms: 90 + 123.765625 = 213.765625 123.765625 + -22.25x + x2 = 213.765625 Factor a perfect square on the left side: (x + -11.125)(x + -11.125) = 213.765625 Calculate the square root of the right side: 14.620725871 Break this problem into two subproblems by setting (x + -11.125) equal to 14.620725871 and -14.620725871.Subproblem 1
x + -11.125 = 14.620725871 Simplifying x + -11.125 = 14.620725871 Reorder the terms: -11.125 + x = 14.620725871 Solving -11.125 + x = 14.620725871 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.125' to each side of the equation. -11.125 + 11.125 + x = 14.620725871 + 11.125 Combine like terms: -11.125 + 11.125 = 0.000 0.000 + x = 14.620725871 + 11.125 x = 14.620725871 + 11.125 Combine like terms: 14.620725871 + 11.125 = 25.745725871 x = 25.745725871 Simplifying x = 25.745725871Subproblem 2
x + -11.125 = -14.620725871 Simplifying x + -11.125 = -14.620725871 Reorder the terms: -11.125 + x = -14.620725871 Solving -11.125 + x = -14.620725871 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.125' to each side of the equation. -11.125 + 11.125 + x = -14.620725871 + 11.125 Combine like terms: -11.125 + 11.125 = 0.000 0.000 + x = -14.620725871 + 11.125 x = -14.620725871 + 11.125 Combine like terms: -14.620725871 + 11.125 = -3.495725871 x = -3.495725871 Simplifying x = -3.495725871Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.745725871, -3.495725871}
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