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Simplifying 8 = 4x2 + 4x + -4 Reorder the terms: 8 = -4 + 4x + 4x2 Solving 8 = -4 + 4x + 4x2 Solving for variable 'x'. Combine like terms: 8 + 4 = 12 12 + -4x + -4x2 = -4 + 4x + 4x2 + 4 + -4x + -4x2 Reorder the terms: 12 + -4x + -4x2 = -4 + 4 + 4x + -4x + 4x2 + -4x2 Combine like terms: -4 + 4 = 0 12 + -4x + -4x2 = 0 + 4x + -4x + 4x2 + -4x2 12 + -4x + -4x2 = 4x + -4x + 4x2 + -4x2 Combine like terms: 4x + -4x = 0 12 + -4x + -4x2 = 0 + 4x2 + -4x2 12 + -4x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 12 + -4x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(3 + -1x + -1x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(3 + -1x + -1x2)' equal to zero and attempt to solve: Simplifying 3 + -1x + -1x2 = 0 Solving 3 + -1x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -3 + x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + x + x2 = 0 + 3 x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 x + x2 = 3 The x term is x. 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. + 0.25 + x2 = 3 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 3 + 0.25 Combine like terms: 3 + 0.25 = 3.25 1.25 + x2 = 3.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 3.25 Calculate the square root of the right side: 1.802775638 Break this problem into two subproblems by setting (x + 0.5) equal to 1.802775638 and -1.802775638.Subproblem 1
x + 0.5 = 1.802775638 Simplifying x + 0.5 = 1.802775638 Reorder the terms: 0.5 + x = 1.802775638 Solving 0.5 + x = 1.802775638 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 = 1.802775638 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.802775638 + -0.5 x = 1.802775638 + -0.5 Combine like terms: 1.802775638 + -0.5 = 1.302775638 x = 1.302775638 Simplifying x = 1.302775638Subproblem 2
x + 0.5 = -1.802775638 Simplifying x + 0.5 = -1.802775638 Reorder the terms: 0.5 + x = -1.802775638 Solving 0.5 + x = -1.802775638 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 = -1.802775638 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.802775638 + -0.5 x = -1.802775638 + -0.5 Combine like terms: -1.802775638 + -0.5 = -2.302775638 x = -2.302775638 Simplifying x = -2.302775638Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.302775638, -2.302775638}Solution
x = {1.302775638, -2.302775638}
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