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Simplifying 0 = -8x2 + 7x + 4 Reorder the terms: 0 = 4 + 7x + -8x2 Solving 0 = 4 + 7x + -8x2 Solving for variable 'x'. Combine like terms: 0 + -4 = -4 -4 + -7x + 8x2 = 4 + 7x + -8x2 + -4 + -7x + 8x2 Reorder the terms: -4 + -7x + 8x2 = 4 + -4 + 7x + -7x + -8x2 + 8x2 Combine like terms: 4 + -4 = 0 -4 + -7x + 8x2 = 0 + 7x + -7x + -8x2 + 8x2 -4 + -7x + 8x2 = 7x + -7x + -8x2 + 8x2 Combine like terms: 7x + -7x = 0 -4 + -7x + 8x2 = 0 + -8x2 + 8x2 -4 + -7x + 8x2 = -8x2 + 8x2 Combine like terms: -8x2 + 8x2 = 0 -4 + -7x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.5 + -0.875x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -0.875x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -0.875x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -0.875x + x2 = 0 + 0.5 -0.875x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -0.875x + x2 = 0.5 The x term is -0.875x. Take half its coefficient (-0.4375). Square it (0.19140625) and add it to both sides. Add '0.19140625' to each side of the equation. -0.875x + 0.19140625 + x2 = 0.5 + 0.19140625 Reorder the terms: 0.19140625 + -0.875x + x2 = 0.5 + 0.19140625 Combine like terms: 0.5 + 0.19140625 = 0.69140625 0.19140625 + -0.875x + x2 = 0.69140625 Factor a perfect square on the left side: (x + -0.4375)(x + -0.4375) = 0.69140625 Calculate the square root of the right side: 0.831508418 Break this problem into two subproblems by setting (x + -0.4375) equal to 0.831508418 and -0.831508418.Subproblem 1
x + -0.4375 = 0.831508418 Simplifying x + -0.4375 = 0.831508418 Reorder the terms: -0.4375 + x = 0.831508418 Solving -0.4375 + x = 0.831508418 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4375' to each side of the equation. -0.4375 + 0.4375 + x = 0.831508418 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + x = 0.831508418 + 0.4375 x = 0.831508418 + 0.4375 Combine like terms: 0.831508418 + 0.4375 = 1.269008418 x = 1.269008418 Simplifying x = 1.269008418Subproblem 2
x + -0.4375 = -0.831508418 Simplifying x + -0.4375 = -0.831508418 Reorder the terms: -0.4375 + x = -0.831508418 Solving -0.4375 + x = -0.831508418 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4375' to each side of the equation. -0.4375 + 0.4375 + x = -0.831508418 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + x = -0.831508418 + 0.4375 x = -0.831508418 + 0.4375 Combine like terms: -0.831508418 + 0.4375 = -0.394008418 x = -0.394008418 Simplifying x = -0.394008418Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.269008418, -0.394008418}
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