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Simplifying 4x2 + -69x + 26 = 7x2 + -8 Reorder the terms: 26 + -69x + 4x2 = 7x2 + -8 Reorder the terms: 26 + -69x + 4x2 = -8 + 7x2 Solving 26 + -69x + 4x2 = -8 + 7x2 Solving for variable 'x'. Reorder the terms: 26 + 8 + -69x + 4x2 + -7x2 = -8 + 7x2 + 8 + -7x2 Combine like terms: 26 + 8 = 34 34 + -69x + 4x2 + -7x2 = -8 + 7x2 + 8 + -7x2 Combine like terms: 4x2 + -7x2 = -3x2 34 + -69x + -3x2 = -8 + 7x2 + 8 + -7x2 Reorder the terms: 34 + -69x + -3x2 = -8 + 8 + 7x2 + -7x2 Combine like terms: -8 + 8 = 0 34 + -69x + -3x2 = 0 + 7x2 + -7x2 34 + -69x + -3x2 = 7x2 + -7x2 Combine like terms: 7x2 + -7x2 = 0 34 + -69x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -11.33333333 + 23x + x2 = 0 Move the constant term to the right: Add '11.33333333' to each side of the equation. -11.33333333 + 23x + 11.33333333 + x2 = 0 + 11.33333333 Reorder the terms: -11.33333333 + 11.33333333 + 23x + x2 = 0 + 11.33333333 Combine like terms: -11.33333333 + 11.33333333 = 0.00000000 0.00000000 + 23x + x2 = 0 + 11.33333333 23x + x2 = 0 + 11.33333333 Combine like terms: 0 + 11.33333333 = 11.33333333 23x + x2 = 11.33333333 The x term is 23x. Take half its coefficient (11.5). Square it (132.25) and add it to both sides. Add '132.25' to each side of the equation. 23x + 132.25 + x2 = 11.33333333 + 132.25 Reorder the terms: 132.25 + 23x + x2 = 11.33333333 + 132.25 Combine like terms: 11.33333333 + 132.25 = 143.58333333 132.25 + 23x + x2 = 143.58333333 Factor a perfect square on the left side: (x + 11.5)(x + 11.5) = 143.58333333 Calculate the square root of the right side: 11.982626312 Break this problem into two subproblems by setting (x + 11.5) equal to 11.982626312 and -11.982626312.Subproblem 1
x + 11.5 = 11.982626312 Simplifying x + 11.5 = 11.982626312 Reorder the terms: 11.5 + x = 11.982626312 Solving 11.5 + x = 11.982626312 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.5' to each side of the equation. 11.5 + -11.5 + x = 11.982626312 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + x = 11.982626312 + -11.5 x = 11.982626312 + -11.5 Combine like terms: 11.982626312 + -11.5 = 0.482626312 x = 0.482626312 Simplifying x = 0.482626312Subproblem 2
x + 11.5 = -11.982626312 Simplifying x + 11.5 = -11.982626312 Reorder the terms: 11.5 + x = -11.982626312 Solving 11.5 + x = -11.982626312 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.5' to each side of the equation. 11.5 + -11.5 + x = -11.982626312 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + x = -11.982626312 + -11.5 x = -11.982626312 + -11.5 Combine like terms: -11.982626312 + -11.5 = -23.482626312 x = -23.482626312 Simplifying x = -23.482626312Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.482626312, -23.482626312}
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