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Simplifying 7(x + -4) * 8x = 12 + 14 Reorder the terms: 7(-4 + x) * 8x = 12 + 14 Reorder the terms for easier multiplication: 7 * 8x(-4 + x) = 12 + 14 Multiply 7 * 8 56x(-4 + x) = 12 + 14 (-4 * 56x + x * 56x) = 12 + 14 (-224x + 56x2) = 12 + 14 Combine like terms: 12 + 14 = 26 -224x + 56x2 = 26 Solving -224x + 56x2 = 26 Solving for variable 'x'. Reorder the terms: -26 + -224x + 56x2 = 26 + -26 Combine like terms: 26 + -26 = 0 -26 + -224x + 56x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-13 + -112x + 28x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-13 + -112x + 28x2)' equal to zero and attempt to solve: Simplifying -13 + -112x + 28x2 = 0 Solving -13 + -112x + 28x2 = 0 Begin completing the square. Divide all terms by 28 the coefficient of the squared term: Divide each side by '28'. -0.4642857143 + -4x + x2 = 0 Move the constant term to the right: Add '0.4642857143' to each side of the equation. -0.4642857143 + -4x + 0.4642857143 + x2 = 0 + 0.4642857143 Reorder the terms: -0.4642857143 + 0.4642857143 + -4x + x2 = 0 + 0.4642857143 Combine like terms: -0.4642857143 + 0.4642857143 = 0.0000000000 0.0000000000 + -4x + x2 = 0 + 0.4642857143 -4x + x2 = 0 + 0.4642857143 Combine like terms: 0 + 0.4642857143 = 0.4642857143 -4x + x2 = 0.4642857143 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 0.4642857143 + 4 Reorder the terms: 4 + -4x + x2 = 0.4642857143 + 4 Combine like terms: 0.4642857143 + 4 = 4.4642857143 4 + -4x + x2 = 4.4642857143 Factor a perfect square on the left side: (x + -2)(x + -2) = 4.4642857143 Calculate the square root of the right side: 2.112885637 Break this problem into two subproblems by setting (x + -2) equal to 2.112885637 and -2.112885637.Subproblem 1
x + -2 = 2.112885637 Simplifying x + -2 = 2.112885637 Reorder the terms: -2 + x = 2.112885637 Solving -2 + x = 2.112885637 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 2.112885637 + 2 Combine like terms: -2 + 2 = 0 0 + x = 2.112885637 + 2 x = 2.112885637 + 2 Combine like terms: 2.112885637 + 2 = 4.112885637 x = 4.112885637 Simplifying x = 4.112885637Subproblem 2
x + -2 = -2.112885637 Simplifying x + -2 = -2.112885637 Reorder the terms: -2 + x = -2.112885637 Solving -2 + x = -2.112885637 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -2.112885637 + 2 Combine like terms: -2 + 2 = 0 0 + x = -2.112885637 + 2 x = -2.112885637 + 2 Combine like terms: -2.112885637 + 2 = -0.112885637 x = -0.112885637 Simplifying x = -0.112885637Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.112885637, -0.112885637}Solution
x = {4.112885637, -0.112885637}
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