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Simplifying 0 = -8x2 + 8x + 7 Reorder the terms: 0 = 7 + 8x + -8x2 Solving 0 = 7 + 8x + -8x2 Solving for variable 'x'. Combine like terms: 0 + -7 = -7 -7 + -8x + 8x2 = 7 + 8x + -8x2 + -7 + -8x + 8x2 Reorder the terms: -7 + -8x + 8x2 = 7 + -7 + 8x + -8x + -8x2 + 8x2 Combine like terms: 7 + -7 = 0 -7 + -8x + 8x2 = 0 + 8x + -8x + -8x2 + 8x2 -7 + -8x + 8x2 = 8x + -8x + -8x2 + 8x2 Combine like terms: 8x + -8x = 0 -7 + -8x + 8x2 = 0 + -8x2 + 8x2 -7 + -8x + 8x2 = -8x2 + 8x2 Combine like terms: -8x2 + 8x2 = 0 -7 + -8x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.875 + -1x + x2 = 0 Move the constant term to the right: Add '0.875' to each side of the equation. -0.875 + -1x + 0.875 + x2 = 0 + 0.875 Reorder the terms: -0.875 + 0.875 + -1x + x2 = 0 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + -1x + x2 = 0 + 0.875 -1x + x2 = 0 + 0.875 Combine like terms: 0 + 0.875 = 0.875 -1x + x2 = 0.875 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 0.875 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 0.875 + 0.25 Combine like terms: 0.875 + 0.25 = 1.125 0.25 + -1x + x2 = 1.125 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 1.125 Calculate the square root of the right side: 1.060660172 Break this problem into two subproblems by setting (x + -0.5) equal to 1.060660172 and -1.060660172.Subproblem 1
x + -0.5 = 1.060660172 Simplifying x + -0.5 = 1.060660172 Reorder the terms: -0.5 + x = 1.060660172 Solving -0.5 + x = 1.060660172 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 1.060660172 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 1.060660172 + 0.5 x = 1.060660172 + 0.5 Combine like terms: 1.060660172 + 0.5 = 1.560660172 x = 1.560660172 Simplifying x = 1.560660172Subproblem 2
x + -0.5 = -1.060660172 Simplifying x + -0.5 = -1.060660172 Reorder the terms: -0.5 + x = -1.060660172 Solving -0.5 + x = -1.060660172 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -1.060660172 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -1.060660172 + 0.5 x = -1.060660172 + 0.5 Combine like terms: -1.060660172 + 0.5 = -0.560660172 x = -0.560660172 Simplifying x = -0.560660172Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.560660172, -0.560660172}
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