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Simplifying 8x2 + 14x + -8 = 0 Reorder the terms: -8 + 14x + 8x2 = 0 Solving -8 + 14x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + 7x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + 7x + 4x2)' equal to zero and attempt to solve: Simplifying -4 + 7x + 4x2 = 0 Solving -4 + 7x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1 + 1.75x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 1.75x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 1.75x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 1.75x + x2 = 0 + 1 1.75x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 1.75x + x2 = 1 The x term is 1.75x. Take half its coefficient (0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. 1.75x + 0.765625 + x2 = 1 + 0.765625 Reorder the terms: 0.765625 + 1.75x + x2 = 1 + 0.765625 Combine like terms: 1 + 0.765625 = 1.765625 0.765625 + 1.75x + x2 = 1.765625 Factor a perfect square on the left side: (x + 0.875)(x + 0.875) = 1.765625 Calculate the square root of the right side: 1.328768227 Break this problem into two subproblems by setting (x + 0.875) equal to 1.328768227 and -1.328768227.Subproblem 1
x + 0.875 = 1.328768227 Simplifying x + 0.875 = 1.328768227 Reorder the terms: 0.875 + x = 1.328768227 Solving 0.875 + x = 1.328768227 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + x = 1.328768227 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = 1.328768227 + -0.875 x = 1.328768227 + -0.875 Combine like terms: 1.328768227 + -0.875 = 0.453768227 x = 0.453768227 Simplifying x = 0.453768227Subproblem 2
x + 0.875 = -1.328768227 Simplifying x + 0.875 = -1.328768227 Reorder the terms: 0.875 + x = -1.328768227 Solving 0.875 + x = -1.328768227 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + x = -1.328768227 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = -1.328768227 + -0.875 x = -1.328768227 + -0.875 Combine like terms: -1.328768227 + -0.875 = -2.203768227 x = -2.203768227 Simplifying x = -2.203768227Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.453768227, -2.203768227}Solution
x = {0.453768227, -2.203768227}
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