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Simplifying 11x2 + 3x + -15 = -5 Reorder the terms: -15 + 3x + 11x2 = -5 Solving -15 + 3x + 11x2 = -5 Solving for variable 'x'. Reorder the terms: -15 + 5 + 3x + 11x2 = -5 + 5 Combine like terms: -15 + 5 = -10 -10 + 3x + 11x2 = -5 + 5 Combine like terms: -5 + 5 = 0 -10 + 3x + 11x2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -0.9090909091 + 0.2727272727x + x2 = 0 Move the constant term to the right: Add '0.9090909091' to each side of the equation. -0.9090909091 + 0.2727272727x + 0.9090909091 + x2 = 0 + 0.9090909091 Reorder the terms: -0.9090909091 + 0.9090909091 + 0.2727272727x + x2 = 0 + 0.9090909091 Combine like terms: -0.9090909091 + 0.9090909091 = 0.0000000000 0.0000000000 + 0.2727272727x + x2 = 0 + 0.9090909091 0.2727272727x + x2 = 0 + 0.9090909091 Combine like terms: 0 + 0.9090909091 = 0.9090909091 0.2727272727x + x2 = 0.9090909091 The x term is 0.2727272727x. Take half its coefficient (0.1363636364). Square it (0.01859504133) and add it to both sides. Add '0.01859504133' to each side of the equation. 0.2727272727x + 0.01859504133 + x2 = 0.9090909091 + 0.01859504133 Reorder the terms: 0.01859504133 + 0.2727272727x + x2 = 0.9090909091 + 0.01859504133 Combine like terms: 0.9090909091 + 0.01859504133 = 0.92768595043 0.01859504133 + 0.2727272727x + x2 = 0.92768595043 Factor a perfect square on the left side: (x + 0.1363636364)(x + 0.1363636364) = 0.92768595043 Calculate the square root of the right side: 0.96316455 Break this problem into two subproblems by setting (x + 0.1363636364) equal to 0.96316455 and -0.96316455.Subproblem 1
x + 0.1363636364 = 0.96316455 Simplifying x + 0.1363636364 = 0.96316455 Reorder the terms: 0.1363636364 + x = 0.96316455 Solving 0.1363636364 + x = 0.96316455 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1363636364' to each side of the equation. 0.1363636364 + -0.1363636364 + x = 0.96316455 + -0.1363636364 Combine like terms: 0.1363636364 + -0.1363636364 = 0.0000000000 0.0000000000 + x = 0.96316455 + -0.1363636364 x = 0.96316455 + -0.1363636364 Combine like terms: 0.96316455 + -0.1363636364 = 0.8268009136 x = 0.8268009136 Simplifying x = 0.8268009136Subproblem 2
x + 0.1363636364 = -0.96316455 Simplifying x + 0.1363636364 = -0.96316455 Reorder the terms: 0.1363636364 + x = -0.96316455 Solving 0.1363636364 + x = -0.96316455 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1363636364' to each side of the equation. 0.1363636364 + -0.1363636364 + x = -0.96316455 + -0.1363636364 Combine like terms: 0.1363636364 + -0.1363636364 = 0.0000000000 0.0000000000 + x = -0.96316455 + -0.1363636364 x = -0.96316455 + -0.1363636364 Combine like terms: -0.96316455 + -0.1363636364 = -1.0995281864 x = -1.0995281864 Simplifying x = -1.0995281864Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8268009136, -1.0995281864}
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