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Simplifying 4x2 + 56x + -42 = 0 Reorder the terms: -42 + 56x + 4x2 = 0 Solving -42 + 56x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-21 + 28x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-21 + 28x + 2x2)' equal to zero and attempt to solve: Simplifying -21 + 28x + 2x2 = 0 Solving -21 + 28x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -10.5 + 14x + x2 = 0 Move the constant term to the right: Add '10.5' to each side of the equation. -10.5 + 14x + 10.5 + x2 = 0 + 10.5 Reorder the terms: -10.5 + 10.5 + 14x + x2 = 0 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + 14x + x2 = 0 + 10.5 14x + x2 = 0 + 10.5 Combine like terms: 0 + 10.5 = 10.5 14x + x2 = 10.5 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 = 10.5 + 49 Reorder the terms: 49 + 14x + x2 = 10.5 + 49 Combine like terms: 10.5 + 49 = 59.5 49 + 14x + x2 = 59.5 Factor a perfect square on the left side: (x + 7)(x + 7) = 59.5 Calculate the square root of the right side: 7.71362431 Break this problem into two subproblems by setting (x + 7) equal to 7.71362431 and -7.71362431.Subproblem 1
x + 7 = 7.71362431 Simplifying x + 7 = 7.71362431 Reorder the terms: 7 + x = 7.71362431 Solving 7 + x = 7.71362431 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 = 7.71362431 + -7 Combine like terms: 7 + -7 = 0 0 + x = 7.71362431 + -7 x = 7.71362431 + -7 Combine like terms: 7.71362431 + -7 = 0.71362431 x = 0.71362431 Simplifying x = 0.71362431Subproblem 2
x + 7 = -7.71362431 Simplifying x + 7 = -7.71362431 Reorder the terms: 7 + x = -7.71362431 Solving 7 + x = -7.71362431 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 = -7.71362431 + -7 Combine like terms: 7 + -7 = 0 0 + x = -7.71362431 + -7 x = -7.71362431 + -7 Combine like terms: -7.71362431 + -7 = -14.71362431 x = -14.71362431 Simplifying x = -14.71362431Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.71362431, -14.71362431}Solution
x = {0.71362431, -14.71362431}
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