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Simplifying -1x2 + -7x + 12.25 = 13 Reorder the terms: 12.25 + -7x + -1x2 = 13 Solving 12.25 + -7x + -1x2 = 13 Solving for variable 'x'. Reorder the terms: 12.25 + -13 + -7x + -1x2 = 13 + -13 Combine like terms: 12.25 + -13 = -0.75 -0.75 + -7x + -1x2 = 13 + -13 Combine like terms: 13 + -13 = 0 -0.75 + -7x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 0.75 + 7x + x2 = 0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + 7x + -0.75 + x2 = 0 + -0.75 Reorder the terms: 0.75 + -0.75 + 7x + x2 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + 7x + x2 = 0 + -0.75 7x + x2 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 7x + x2 = -0.75 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 = -0.75 + 12.25 Reorder the terms: 12.25 + 7x + x2 = -0.75 + 12.25 Combine like terms: -0.75 + 12.25 = 11.5 12.25 + 7x + x2 = 11.5 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 11.5 Calculate the square root of the right side: 3.391164992 Break this problem into two subproblems by setting (x + 3.5) equal to 3.391164992 and -3.391164992.Subproblem 1
x + 3.5 = 3.391164992 Simplifying x + 3.5 = 3.391164992 Reorder the terms: 3.5 + x = 3.391164992 Solving 3.5 + x = 3.391164992 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 = 3.391164992 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 3.391164992 + -3.5 x = 3.391164992 + -3.5 Combine like terms: 3.391164992 + -3.5 = -0.108835008 x = -0.108835008 Simplifying x = -0.108835008Subproblem 2
x + 3.5 = -3.391164992 Simplifying x + 3.5 = -3.391164992 Reorder the terms: 3.5 + x = -3.391164992 Solving 3.5 + x = -3.391164992 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 = -3.391164992 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -3.391164992 + -3.5 x = -3.391164992 + -3.5 Combine like terms: -3.391164992 + -3.5 = -6.891164992 x = -6.891164992 Simplifying x = -6.891164992Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.108835008, -6.891164992}
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