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Simplifying 8x2 + 14x + -6 = 0 Reorder the terms: -6 + 14x + 8x2 = 0 Solving -6 + 14x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + 7x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + 7x + 4x2)' equal to zero and attempt to solve: Simplifying -3 + 7x + 4x2 = 0 Solving -3 + 7x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.75 + 1.75x + x2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + 1.75x + 0.75 + x2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + 1.75x + x2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + 1.75x + x2 = 0 + 0.75 1.75x + x2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 1.75x + x2 = 0.75 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 = 0.75 + 0.765625 Reorder the terms: 0.765625 + 1.75x + x2 = 0.75 + 0.765625 Combine like terms: 0.75 + 0.765625 = 1.515625 0.765625 + 1.75x + x2 = 1.515625 Factor a perfect square on the left side: (x + 0.875)(x + 0.875) = 1.515625 Calculate the square root of the right side: 1.231107225 Break this problem into two subproblems by setting (x + 0.875) equal to 1.231107225 and -1.231107225.Subproblem 1
x + 0.875 = 1.231107225 Simplifying x + 0.875 = 1.231107225 Reorder the terms: 0.875 + x = 1.231107225 Solving 0.875 + x = 1.231107225 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 = 1.231107225 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = 1.231107225 + -0.875 x = 1.231107225 + -0.875 Combine like terms: 1.231107225 + -0.875 = 0.356107225 x = 0.356107225 Simplifying x = 0.356107225Subproblem 2
x + 0.875 = -1.231107225 Simplifying x + 0.875 = -1.231107225 Reorder the terms: 0.875 + x = -1.231107225 Solving 0.875 + x = -1.231107225 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 = -1.231107225 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = -1.231107225 + -0.875 x = -1.231107225 + -0.875 Combine like terms: -1.231107225 + -0.875 = -2.106107225 x = -2.106107225 Simplifying x = -2.106107225Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.356107225, -2.106107225}Solution
x = {0.356107225, -2.106107225}
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