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Simplifying 4x2 + -56x + 180 = 58 Reorder the terms: 180 + -56x + 4x2 = 58 Solving 180 + -56x + 4x2 = 58 Solving for variable 'x'. Reorder the terms: 180 + -58 + -56x + 4x2 = 58 + -58 Combine like terms: 180 + -58 = 122 122 + -56x + 4x2 = 58 + -58 Combine like terms: 58 + -58 = 0 122 + -56x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(61 + -28x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(61 + -28x + 2x2)' equal to zero and attempt to solve: Simplifying 61 + -28x + 2x2 = 0 Solving 61 + -28x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 30.5 + -14x + x2 = 0 Move the constant term to the right: Add '-30.5' to each side of the equation. 30.5 + -14x + -30.5 + x2 = 0 + -30.5 Reorder the terms: 30.5 + -30.5 + -14x + x2 = 0 + -30.5 Combine like terms: 30.5 + -30.5 = 0.0 0.0 + -14x + x2 = 0 + -30.5 -14x + x2 = 0 + -30.5 Combine like terms: 0 + -30.5 = -30.5 -14x + x2 = -30.5 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 = -30.5 + 49 Reorder the terms: 49 + -14x + x2 = -30.5 + 49 Combine like terms: -30.5 + 49 = 18.5 49 + -14x + x2 = 18.5 Factor a perfect square on the left side: (x + -7)(x + -7) = 18.5 Calculate the square root of the right side: 4.301162634 Break this problem into two subproblems by setting (x + -7) equal to 4.301162634 and -4.301162634.Subproblem 1
x + -7 = 4.301162634 Simplifying x + -7 = 4.301162634 Reorder the terms: -7 + x = 4.301162634 Solving -7 + x = 4.301162634 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 = 4.301162634 + 7 Combine like terms: -7 + 7 = 0 0 + x = 4.301162634 + 7 x = 4.301162634 + 7 Combine like terms: 4.301162634 + 7 = 11.301162634 x = 11.301162634 Simplifying x = 11.301162634Subproblem 2
x + -7 = -4.301162634 Simplifying x + -7 = -4.301162634 Reorder the terms: -7 + x = -4.301162634 Solving -7 + x = -4.301162634 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 = -4.301162634 + 7 Combine like terms: -7 + 7 = 0 0 + x = -4.301162634 + 7 x = -4.301162634 + 7 Combine like terms: -4.301162634 + 7 = 2.698837366 x = 2.698837366 Simplifying x = 2.698837366Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.301162634, 2.698837366}Solution
x = {11.301162634, 2.698837366}
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