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Simplifying 236 + -15x + 2x2 = 360 Solving 236 + -15x + 2x2 = 360 Solving for variable 'x'. Reorder the terms: 236 + -360 + -15x + 2x2 = 360 + -360 Combine like terms: 236 + -360 = -124 -124 + -15x + 2x2 = 360 + -360 Combine like terms: 360 + -360 = 0 -124 + -15x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -62 + -7.5x + x2 = 0 Move the constant term to the right: Add '62' to each side of the equation. -62 + -7.5x + 62 + x2 = 0 + 62 Reorder the terms: -62 + 62 + -7.5x + x2 = 0 + 62 Combine like terms: -62 + 62 = 0 0 + -7.5x + x2 = 0 + 62 -7.5x + x2 = 0 + 62 Combine like terms: 0 + 62 = 62 -7.5x + x2 = 62 The x term is -7.5x. Take half its coefficient (-3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. -7.5x + 14.0625 + x2 = 62 + 14.0625 Reorder the terms: 14.0625 + -7.5x + x2 = 62 + 14.0625 Combine like terms: 62 + 14.0625 = 76.0625 14.0625 + -7.5x + x2 = 76.0625 Factor a perfect square on the left side: (x + -3.75)(x + -3.75) = 76.0625 Calculate the square root of the right side: 8.721381771 Break this problem into two subproblems by setting (x + -3.75) equal to 8.721381771 and -8.721381771.Subproblem 1
x + -3.75 = 8.721381771 Simplifying x + -3.75 = 8.721381771 Reorder the terms: -3.75 + x = 8.721381771 Solving -3.75 + x = 8.721381771 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x = 8.721381771 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = 8.721381771 + 3.75 x = 8.721381771 + 3.75 Combine like terms: 8.721381771 + 3.75 = 12.471381771 x = 12.471381771 Simplifying x = 12.471381771Subproblem 2
x + -3.75 = -8.721381771 Simplifying x + -3.75 = -8.721381771 Reorder the terms: -3.75 + x = -8.721381771 Solving -3.75 + x = -8.721381771 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x = -8.721381771 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = -8.721381771 + 3.75 x = -8.721381771 + 3.75 Combine like terms: -8.721381771 + 3.75 = -4.971381771 x = -4.971381771 Simplifying x = -4.971381771Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.471381771, -4.971381771}
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