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Simplifying 4x2 + -56x + 190 = 0 Reorder the terms: 190 + -56x + 4x2 = 0 Solving 190 + -56x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(95 + -28x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(95 + -28x + 2x2)' equal to zero and attempt to solve: Simplifying 95 + -28x + 2x2 = 0 Solving 95 + -28x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 47.5 + -14x + x2 = 0 Move the constant term to the right: Add '-47.5' to each side of the equation. 47.5 + -14x + -47.5 + x2 = 0 + -47.5 Reorder the terms: 47.5 + -47.5 + -14x + x2 = 0 + -47.5 Combine like terms: 47.5 + -47.5 = 0.0 0.0 + -14x + x2 = 0 + -47.5 -14x + x2 = 0 + -47.5 Combine like terms: 0 + -47.5 = -47.5 -14x + x2 = -47.5 The x term is -14x. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14x + 49 + x2 = -47.5 + 49 Reorder the terms: 49 + -14x + x2 = -47.5 + 49 Combine like terms: -47.5 + 49 = 1.5 49 + -14x + x2 = 1.5 Factor a perfect square on the left side: (x + -7)(x + -7) = 1.5 Calculate the square root of the right side: 1.224744871 Break this problem into two subproblems by setting (x + -7) equal to 1.224744871 and -1.224744871.Subproblem 1
x + -7 = 1.224744871 Simplifying x + -7 = 1.224744871 Reorder the terms: -7 + x = 1.224744871 Solving -7 + x = 1.224744871 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = 1.224744871 + 7 Combine like terms: -7 + 7 = 0 0 + x = 1.224744871 + 7 x = 1.224744871 + 7 Combine like terms: 1.224744871 + 7 = 8.224744871 x = 8.224744871 Simplifying x = 8.224744871Subproblem 2
x + -7 = -1.224744871 Simplifying x + -7 = -1.224744871 Reorder the terms: -7 + x = -1.224744871 Solving -7 + x = -1.224744871 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = -1.224744871 + 7 Combine like terms: -7 + 7 = 0 0 + x = -1.224744871 + 7 x = -1.224744871 + 7 Combine like terms: -1.224744871 + 7 = 5.775255129 x = 5.775255129 Simplifying x = 5.775255129Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.224744871, 5.775255129}Solution
x = {8.224744871, 5.775255129}
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