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Simplifying 8x2 + -16x + -36 = -10 Reorder the terms: -36 + -16x + 8x2 = -10 Solving -36 + -16x + 8x2 = -10 Solving for variable 'x'. Reorder the terms: -36 + 10 + -16x + 8x2 = -10 + 10 Combine like terms: -36 + 10 = -26 -26 + -16x + 8x2 = -10 + 10 Combine like terms: -10 + 10 = 0 -26 + -16x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-13 + -8x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-13 + -8x + 4x2)' equal to zero and attempt to solve: Simplifying -13 + -8x + 4x2 = 0 Solving -13 + -8x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3.25 + -2x + x2 = 0 Move the constant term to the right: Add '3.25' to each side of the equation. -3.25 + -2x + 3.25 + x2 = 0 + 3.25 Reorder the terms: -3.25 + 3.25 + -2x + x2 = 0 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + -2x + x2 = 0 + 3.25 -2x + x2 = 0 + 3.25 Combine like terms: 0 + 3.25 = 3.25 -2x + x2 = 3.25 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 = 3.25 + 1 Reorder the terms: 1 + -2x + x2 = 3.25 + 1 Combine like terms: 3.25 + 1 = 4.25 1 + -2x + x2 = 4.25 Factor a perfect square on the left side: (x + -1)(x + -1) = 4.25 Calculate the square root of the right side: 2.061552813 Break this problem into two subproblems by setting (x + -1) equal to 2.061552813 and -2.061552813.Subproblem 1
x + -1 = 2.061552813 Simplifying x + -1 = 2.061552813 Reorder the terms: -1 + x = 2.061552813 Solving -1 + x = 2.061552813 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 = 2.061552813 + 1 Combine like terms: -1 + 1 = 0 0 + x = 2.061552813 + 1 x = 2.061552813 + 1 Combine like terms: 2.061552813 + 1 = 3.061552813 x = 3.061552813 Simplifying x = 3.061552813Subproblem 2
x + -1 = -2.061552813 Simplifying x + -1 = -2.061552813 Reorder the terms: -1 + x = -2.061552813 Solving -1 + x = -2.061552813 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 = -2.061552813 + 1 Combine like terms: -1 + 1 = 0 0 + x = -2.061552813 + 1 x = -2.061552813 + 1 Combine like terms: -2.061552813 + 1 = -1.061552813 x = -1.061552813 Simplifying x = -1.061552813Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.061552813, -1.061552813}Solution
x = {3.061552813, -1.061552813}
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