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Simplifying 3.08x2 + -15x + -13 = 0 Reorder the terms: -13 + -15x + 3.08x2 = 0 Solving -13 + -15x + 3.08x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3.08 the coefficient of the squared term: Divide each side by '3.08'. -4.220779221 + -4.87012987x + x2 = 0 Move the constant term to the right: Add '4.220779221' to each side of the equation. -4.220779221 + -4.87012987x + 4.220779221 + x2 = 0 + 4.220779221 Reorder the terms: -4.220779221 + 4.220779221 + -4.87012987x + x2 = 0 + 4.220779221 Combine like terms: -4.220779221 + 4.220779221 = 0.000000000 0.000000000 + -4.87012987x + x2 = 0 + 4.220779221 -4.87012987x + x2 = 0 + 4.220779221 Combine like terms: 0 + 4.220779221 = 4.220779221 -4.87012987x + x2 = 4.220779221 The x term is -4.87012987x. Take half its coefficient (-2.435064935). Square it (5.929541238) and add it to both sides. Add '5.929541238' to each side of the equation. -4.87012987x + 5.929541238 + x2 = 4.220779221 + 5.929541238 Reorder the terms: 5.929541238 + -4.87012987x + x2 = 4.220779221 + 5.929541238 Combine like terms: 4.220779221 + 5.929541238 = 10.150320459 5.929541238 + -4.87012987x + x2 = 10.150320459 Factor a perfect square on the left side: (x + -2.435064935)(x + -2.435064935) = 10.150320459 Calculate the square root of the right side: 3.185956757 Break this problem into two subproblems by setting (x + -2.435064935) equal to 3.185956757 and -3.185956757.Subproblem 1
x + -2.435064935 = 3.185956757 Simplifying x + -2.435064935 = 3.185956757 Reorder the terms: -2.435064935 + x = 3.185956757 Solving -2.435064935 + x = 3.185956757 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.435064935' to each side of the equation. -2.435064935 + 2.435064935 + x = 3.185956757 + 2.435064935 Combine like terms: -2.435064935 + 2.435064935 = 0.000000000 0.000000000 + x = 3.185956757 + 2.435064935 x = 3.185956757 + 2.435064935 Combine like terms: 3.185956757 + 2.435064935 = 5.621021692 x = 5.621021692 Simplifying x = 5.621021692Subproblem 2
x + -2.435064935 = -3.185956757 Simplifying x + -2.435064935 = -3.185956757 Reorder the terms: -2.435064935 + x = -3.185956757 Solving -2.435064935 + x = -3.185956757 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.435064935' to each side of the equation. -2.435064935 + 2.435064935 + x = -3.185956757 + 2.435064935 Combine like terms: -2.435064935 + 2.435064935 = 0.000000000 0.000000000 + x = -3.185956757 + 2.435064935 x = -3.185956757 + 2.435064935 Combine like terms: -3.185956757 + 2.435064935 = -0.750891822 x = -0.750891822 Simplifying x = -0.750891822Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.621021692, -0.750891822}
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