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Simplifying 8x2 + 14x + -42 = 0 Reorder the terms: -42 + 14x + 8x2 = 0 Solving -42 + 14x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-21 + 7x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-21 + 7x + 4x2)' equal to zero and attempt to solve: Simplifying -21 + 7x + 4x2 = 0 Solving -21 + 7x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -5.25 + 1.75x + x2 = 0 Move the constant term to the right: Add '5.25' to each side of the equation. -5.25 + 1.75x + 5.25 + x2 = 0 + 5.25 Reorder the terms: -5.25 + 5.25 + 1.75x + x2 = 0 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + 1.75x + x2 = 0 + 5.25 1.75x + x2 = 0 + 5.25 Combine like terms: 0 + 5.25 = 5.25 1.75x + x2 = 5.25 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 = 5.25 + 0.765625 Reorder the terms: 0.765625 + 1.75x + x2 = 5.25 + 0.765625 Combine like terms: 5.25 + 0.765625 = 6.015625 0.765625 + 1.75x + x2 = 6.015625 Factor a perfect square on the left side: (x + 0.875)(x + 0.875) = 6.015625 Calculate the square root of the right side: 2.452677109 Break this problem into two subproblems by setting (x + 0.875) equal to 2.452677109 and -2.452677109.Subproblem 1
x + 0.875 = 2.452677109 Simplifying x + 0.875 = 2.452677109 Reorder the terms: 0.875 + x = 2.452677109 Solving 0.875 + x = 2.452677109 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 = 2.452677109 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = 2.452677109 + -0.875 x = 2.452677109 + -0.875 Combine like terms: 2.452677109 + -0.875 = 1.577677109 x = 1.577677109 Simplifying x = 1.577677109Subproblem 2
x + 0.875 = -2.452677109 Simplifying x + 0.875 = -2.452677109 Reorder the terms: 0.875 + x = -2.452677109 Solving 0.875 + x = -2.452677109 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 = -2.452677109 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = -2.452677109 + -0.875 x = -2.452677109 + -0.875 Combine like terms: -2.452677109 + -0.875 = -3.327677109 x = -3.327677109 Simplifying x = -3.327677109Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.577677109, -3.327677109}Solution
x = {1.577677109, -3.327677109}
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