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Simplifying 8x2 + 56x + -42 = 0 Reorder the terms: -42 + 56x + 8x2 = 0 Solving -42 + 56x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-21 + 28x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-21 + 28x + 4x2)' equal to zero and attempt to solve: Simplifying -21 + 28x + 4x2 = 0 Solving -21 + 28x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -5.25 + 7x + x2 = 0 Move the constant term to the right: Add '5.25' to each side of the equation. -5.25 + 7x + 5.25 + x2 = 0 + 5.25 Reorder the terms: -5.25 + 5.25 + 7x + x2 = 0 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + 7x + x2 = 0 + 5.25 7x + x2 = 0 + 5.25 Combine like terms: 0 + 5.25 = 5.25 7x + x2 = 5.25 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = 5.25 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 5.25 + 12.25 Combine like terms: 5.25 + 12.25 = 17.5 12.25 + 7x + x2 = 17.5 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 17.5 Calculate the square root of the right side: 4.183300133 Break this problem into two subproblems by setting (x + 3.5) equal to 4.183300133 and -4.183300133.Subproblem 1
x + 3.5 = 4.183300133 Simplifying x + 3.5 = 4.183300133 Reorder the terms: 3.5 + x = 4.183300133 Solving 3.5 + x = 4.183300133 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 4.183300133 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 4.183300133 + -3.5 x = 4.183300133 + -3.5 Combine like terms: 4.183300133 + -3.5 = 0.683300133 x = 0.683300133 Simplifying x = 0.683300133Subproblem 2
x + 3.5 = -4.183300133 Simplifying x + 3.5 = -4.183300133 Reorder the terms: 3.5 + x = -4.183300133 Solving 3.5 + x = -4.183300133 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -4.183300133 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -4.183300133 + -3.5 x = -4.183300133 + -3.5 Combine like terms: -4.183300133 + -3.5 = -7.683300133 x = -7.683300133 Simplifying x = -7.683300133Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.683300133, -7.683300133}Solution
x = {0.683300133, -7.683300133}
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