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Simplifying 8x2 + -16x + -70 = 0 Reorder the terms: -70 + -16x + 8x2 = 0 Solving -70 + -16x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-35 + -8x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-35 + -8x + 4x2)' equal to zero and attempt to solve: Simplifying -35 + -8x + 4x2 = 0 Solving -35 + -8x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -8.75 + -2x + x2 = 0 Move the constant term to the right: Add '8.75' to each side of the equation. -8.75 + -2x + 8.75 + x2 = 0 + 8.75 Reorder the terms: -8.75 + 8.75 + -2x + x2 = 0 + 8.75 Combine like terms: -8.75 + 8.75 = 0.00 0.00 + -2x + x2 = 0 + 8.75 -2x + x2 = 0 + 8.75 Combine like terms: 0 + 8.75 = 8.75 -2x + x2 = 8.75 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 8.75 + 1 Reorder the terms: 1 + -2x + x2 = 8.75 + 1 Combine like terms: 8.75 + 1 = 9.75 1 + -2x + x2 = 9.75 Factor a perfect square on the left side: (x + -1)(x + -1) = 9.75 Calculate the square root of the right side: 3.122498999 Break this problem into two subproblems by setting (x + -1) equal to 3.122498999 and -3.122498999.Subproblem 1
x + -1 = 3.122498999 Simplifying x + -1 = 3.122498999 Reorder the terms: -1 + x = 3.122498999 Solving -1 + x = 3.122498999 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 3.122498999 + 1 Combine like terms: -1 + 1 = 0 0 + x = 3.122498999 + 1 x = 3.122498999 + 1 Combine like terms: 3.122498999 + 1 = 4.122498999 x = 4.122498999 Simplifying x = 4.122498999Subproblem 2
x + -1 = -3.122498999 Simplifying x + -1 = -3.122498999 Reorder the terms: -1 + x = -3.122498999 Solving -1 + x = -3.122498999 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -3.122498999 + 1 Combine like terms: -1 + 1 = 0 0 + x = -3.122498999 + 1 x = -3.122498999 + 1 Combine like terms: -3.122498999 + 1 = -2.122498999 x = -2.122498999 Simplifying x = -2.122498999Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.122498999, -2.122498999}Solution
x = {4.122498999, -2.122498999}
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