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Simplifying 2.5x(x + -6) + -1.5((x * x) + 9) = 0 Reorder the terms: 2.5x(-6 + x) + -1.5((x * x) + 9) = 0 (-6 * 2.5x + x * 2.5x) + -1.5((x * x) + 9) = 0 (-15x + 2.5x2) + -1.5((x * x) + 9) = 0 Multiply x * x -15x + 2.5x2 + -1.5((x2) + 9) = 0 -15x + 2.5x2 + -1.5(x2 + 9) = 0 Reorder the terms: -15x + 2.5x2 + -1.5(9 + x2) = 0 -15x + 2.5x2 + (9 * -1.5 + x2 * -1.5) = 0 -15x + 2.5x2 + (-13.5 + -1.5x2) = 0 Reorder the terms: -13.5 + -15x + 2.5x2 + -1.5x2 = 0 Combine like terms: 2.5x2 + -1.5x2 = 1x2 -13.5 + -15x + 1x2 = 0 Solving -13.5 + -15x + 1x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '13.5' to each side of the equation. -13.5 + -15x + 13.5 + x2 = 0 + 13.5 Reorder the terms: -13.5 + 13.5 + -15x + x2 = 0 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + -15x + x2 = 0 + 13.5 -15x + x2 = 0 + 13.5 Combine like terms: 0 + 13.5 = 13.5 -15x + x2 = 13.5 The x term is -15x. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15x + 56.25 + x2 = 13.5 + 56.25 Reorder the terms: 56.25 + -15x + x2 = 13.5 + 56.25 Combine like terms: 13.5 + 56.25 = 69.75 56.25 + -15x + x2 = 69.75 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 69.75 Calculate the square root of the right side: 8.351646544 Break this problem into two subproblems by setting (x + -7.5) equal to 8.351646544 and -8.351646544.Subproblem 1
x + -7.5 = 8.351646544 Simplifying x + -7.5 = 8.351646544 Reorder the terms: -7.5 + x = 8.351646544 Solving -7.5 + x = 8.351646544 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = 8.351646544 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 8.351646544 + 7.5 x = 8.351646544 + 7.5 Combine like terms: 8.351646544 + 7.5 = 15.851646544 x = 15.851646544 Simplifying x = 15.851646544Subproblem 2
x + -7.5 = -8.351646544 Simplifying x + -7.5 = -8.351646544 Reorder the terms: -7.5 + x = -8.351646544 Solving -7.5 + x = -8.351646544 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = -8.351646544 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -8.351646544 + 7.5 x = -8.351646544 + 7.5 Combine like terms: -8.351646544 + 7.5 = -0.851646544 x = -0.851646544 Simplifying x = -0.851646544Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.851646544, -0.851646544}
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