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Simplifying x(4x + -15) + 4(40 + -1x) = 180 Reorder the terms: x(-15 + 4x) + 4(40 + -1x) = 180 (-15 * x + 4x * x) + 4(40 + -1x) = 180 (-15x + 4x2) + 4(40 + -1x) = 180 -15x + 4x2 + (40 * 4 + -1x * 4) = 180 -15x + 4x2 + (160 + -4x) = 180 Reorder the terms: 160 + -15x + -4x + 4x2 = 180 Combine like terms: -15x + -4x = -19x 160 + -19x + 4x2 = 180 Solving 160 + -19x + 4x2 = 180 Solving for variable 'x'. Reorder the terms: 160 + -180 + -19x + 4x2 = 180 + -180 Combine like terms: 160 + -180 = -20 -20 + -19x + 4x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -20 + -19x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -5 + -4.75x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -4.75x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + -4.75x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -4.75x + x2 = 0 + 5 -4.75x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -4.75x + x2 = 5 The x term is -4.75x. Take half its coefficient (-2.375). Square it (5.640625) and add it to both sides. Add '5.640625' to each side of the equation. -4.75x + 5.640625 + x2 = 5 + 5.640625 Reorder the terms: 5.640625 + -4.75x + x2 = 5 + 5.640625 Combine like terms: 5 + 5.640625 = 10.640625 5.640625 + -4.75x + x2 = 10.640625 Factor a perfect square on the left side: (x + -2.375)(x + -2.375) = 10.640625 Calculate the square root of the right side: 3.261997088 Break this problem into two subproblems by setting (x + -2.375) equal to 3.261997088 and -3.261997088.Subproblem 1
x + -2.375 = 3.261997088 Simplifying x + -2.375 = 3.261997088 Reorder the terms: -2.375 + x = 3.261997088 Solving -2.375 + x = 3.261997088 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.375' to each side of the equation. -2.375 + 2.375 + x = 3.261997088 + 2.375 Combine like terms: -2.375 + 2.375 = 0.000 0.000 + x = 3.261997088 + 2.375 x = 3.261997088 + 2.375 Combine like terms: 3.261997088 + 2.375 = 5.636997088 x = 5.636997088 Simplifying x = 5.636997088Subproblem 2
x + -2.375 = -3.261997088 Simplifying x + -2.375 = -3.261997088 Reorder the terms: -2.375 + x = -3.261997088 Solving -2.375 + x = -3.261997088 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.375' to each side of the equation. -2.375 + 2.375 + x = -3.261997088 + 2.375 Combine like terms: -2.375 + 2.375 = 0.000 0.000 + x = -3.261997088 + 2.375 x = -3.261997088 + 2.375 Combine like terms: -3.261997088 + 2.375 = -0.886997088 x = -0.886997088 Simplifying x = -0.886997088Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.636997088, -0.886997088}
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