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Simplifying 10x2 + 52x + 8 = 0 Reorder the terms: 8 + 52x + 10x2 = 0 Solving 8 + 52x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(4 + 26x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4 + 26x + 5x2)' equal to zero and attempt to solve: Simplifying 4 + 26x + 5x2 = 0 Solving 4 + 26x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.8 + 5.2x + x2 = 0 Move the constant term to the right: Add '-0.8' to each side of the equation. 0.8 + 5.2x + -0.8 + x2 = 0 + -0.8 Reorder the terms: 0.8 + -0.8 + 5.2x + x2 = 0 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + 5.2x + x2 = 0 + -0.8 5.2x + x2 = 0 + -0.8 Combine like terms: 0 + -0.8 = -0.8 5.2x + x2 = -0.8 The x term is 5.2x. Take half its coefficient (2.6). Square it (6.76) and add it to both sides. Add '6.76' to each side of the equation. 5.2x + 6.76 + x2 = -0.8 + 6.76 Reorder the terms: 6.76 + 5.2x + x2 = -0.8 + 6.76 Combine like terms: -0.8 + 6.76 = 5.96 6.76 + 5.2x + x2 = 5.96 Factor a perfect square on the left side: (x + 2.6)(x + 2.6) = 5.96 Calculate the square root of the right side: 2.441311123 Break this problem into two subproblems by setting (x + 2.6) equal to 2.441311123 and -2.441311123.Subproblem 1
x + 2.6 = 2.441311123 Simplifying x + 2.6 = 2.441311123 Reorder the terms: 2.6 + x = 2.441311123 Solving 2.6 + x = 2.441311123 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.6' to each side of the equation. 2.6 + -2.6 + x = 2.441311123 + -2.6 Combine like terms: 2.6 + -2.6 = 0.0 0.0 + x = 2.441311123 + -2.6 x = 2.441311123 + -2.6 Combine like terms: 2.441311123 + -2.6 = -0.158688877 x = -0.158688877 Simplifying x = -0.158688877Subproblem 2
x + 2.6 = -2.441311123 Simplifying x + 2.6 = -2.441311123 Reorder the terms: 2.6 + x = -2.441311123 Solving 2.6 + x = -2.441311123 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.6' to each side of the equation. 2.6 + -2.6 + x = -2.441311123 + -2.6 Combine like terms: 2.6 + -2.6 = 0.0 0.0 + x = -2.441311123 + -2.6 x = -2.441311123 + -2.6 Combine like terms: -2.441311123 + -2.6 = -5.041311123 x = -5.041311123 Simplifying x = -5.041311123Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.158688877, -5.041311123}Solution
x = {-0.158688877, -5.041311123}
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