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Simplifying -16x2 + 10x = -775 Reorder the terms: 10x + -16x2 = -775 Solving 10x + -16x2 = -775 Solving for variable 'x'. Reorder the terms: 775 + 10x + -16x2 = -775 + 775 Combine like terms: -775 + 775 = 0 775 + 10x + -16x2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -48.4375 + -0.625x + x2 = 0 Move the constant term to the right: Add '48.4375' to each side of the equation. -48.4375 + -0.625x + 48.4375 + x2 = 0 + 48.4375 Reorder the terms: -48.4375 + 48.4375 + -0.625x + x2 = 0 + 48.4375 Combine like terms: -48.4375 + 48.4375 = 0.0000 0.0000 + -0.625x + x2 = 0 + 48.4375 -0.625x + x2 = 0 + 48.4375 Combine like terms: 0 + 48.4375 = 48.4375 -0.625x + x2 = 48.4375 The x term is -0.625x. Take half its coefficient (-0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. -0.625x + 0.09765625 + x2 = 48.4375 + 0.09765625 Reorder the terms: 0.09765625 + -0.625x + x2 = 48.4375 + 0.09765625 Combine like terms: 48.4375 + 0.09765625 = 48.53515625 0.09765625 + -0.625x + x2 = 48.53515625 Factor a perfect square on the left side: (x + -0.3125)(x + -0.3125) = 48.53515625 Calculate the square root of the right side: 6.966717753 Break this problem into two subproblems by setting (x + -0.3125) equal to 6.966717753 and -6.966717753.Subproblem 1
x + -0.3125 = 6.966717753 Simplifying x + -0.3125 = 6.966717753 Reorder the terms: -0.3125 + x = 6.966717753 Solving -0.3125 + x = 6.966717753 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + x = 6.966717753 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + x = 6.966717753 + 0.3125 x = 6.966717753 + 0.3125 Combine like terms: 6.966717753 + 0.3125 = 7.279217753 x = 7.279217753 Simplifying x = 7.279217753Subproblem 2
x + -0.3125 = -6.966717753 Simplifying x + -0.3125 = -6.966717753 Reorder the terms: -0.3125 + x = -6.966717753 Solving -0.3125 + x = -6.966717753 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + x = -6.966717753 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + x = -6.966717753 + 0.3125 x = -6.966717753 + 0.3125 Combine like terms: -6.966717753 + 0.3125 = -6.654217753 x = -6.654217753 Simplifying x = -6.654217753Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.279217753, -6.654217753}
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