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Simplifying -2x2 + 16x + -15 = 0 Reorder the terms: -15 + 16x + -2x2 = 0 Solving -15 + 16x + -2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 7.5 + -8x + x2 = 0 Move the constant term to the right: Add '-7.5' to each side of the equation. 7.5 + -8x + -7.5 + x2 = 0 + -7.5 Reorder the terms: 7.5 + -7.5 + -8x + x2 = 0 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + -8x + x2 = 0 + -7.5 -8x + x2 = 0 + -7.5 Combine like terms: 0 + -7.5 = -7.5 -8x + x2 = -7.5 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = -7.5 + 16 Reorder the terms: 16 + -8x + x2 = -7.5 + 16 Combine like terms: -7.5 + 16 = 8.5 16 + -8x + x2 = 8.5 Factor a perfect square on the left side: (x + -4)(x + -4) = 8.5 Calculate the square root of the right side: 2.915475947 Break this problem into two subproblems by setting (x + -4) equal to 2.915475947 and -2.915475947.Subproblem 1
x + -4 = 2.915475947 Simplifying x + -4 = 2.915475947 Reorder the terms: -4 + x = 2.915475947 Solving -4 + x = 2.915475947 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 2.915475947 + 4 Combine like terms: -4 + 4 = 0 0 + x = 2.915475947 + 4 x = 2.915475947 + 4 Combine like terms: 2.915475947 + 4 = 6.915475947 x = 6.915475947 Simplifying x = 6.915475947Subproblem 2
x + -4 = -2.915475947 Simplifying x + -4 = -2.915475947 Reorder the terms: -4 + x = -2.915475947 Solving -4 + x = -2.915475947 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -2.915475947 + 4 Combine like terms: -4 + 4 = 0 0 + x = -2.915475947 + 4 x = -2.915475947 + 4 Combine like terms: -2.915475947 + 4 = 1.084524053 x = 1.084524053 Simplifying x = 1.084524053Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.915475947, 1.084524053}
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