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Simplifying 4x2 + -13x + 7 + -9x2 + -22x + -16 = 0 Reorder the terms: 7 + -16 + -13x + -22x + 4x2 + -9x2 = 0 Combine like terms: 7 + -16 = -9 -9 + -13x + -22x + 4x2 + -9x2 = 0 Combine like terms: -13x + -22x = -35x -9 + -35x + 4x2 + -9x2 = 0 Combine like terms: 4x2 + -9x2 = -5x2 -9 + -35x + -5x2 = 0 Solving -9 + -35x + -5x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(9 + 35x + 5x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(9 + 35x + 5x2)' equal to zero and attempt to solve: Simplifying 9 + 35x + 5x2 = 0 Solving 9 + 35x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1.8 + 7x + x2 = 0 Move the constant term to the right: Add '-1.8' to each side of the equation. 1.8 + 7x + -1.8 + x2 = 0 + -1.8 Reorder the terms: 1.8 + -1.8 + 7x + x2 = 0 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + 7x + x2 = 0 + -1.8 7x + x2 = 0 + -1.8 Combine like terms: 0 + -1.8 = -1.8 7x + x2 = -1.8 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 = -1.8 + 12.25 Reorder the terms: 12.25 + 7x + x2 = -1.8 + 12.25 Combine like terms: -1.8 + 12.25 = 10.45 12.25 + 7x + x2 = 10.45 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 10.45 Calculate the square root of the right side: 3.232645975 Break this problem into two subproblems by setting (x + 3.5) equal to 3.232645975 and -3.232645975.Subproblem 1
x + 3.5 = 3.232645975 Simplifying x + 3.5 = 3.232645975 Reorder the terms: 3.5 + x = 3.232645975 Solving 3.5 + x = 3.232645975 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 = 3.232645975 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 3.232645975 + -3.5 x = 3.232645975 + -3.5 Combine like terms: 3.232645975 + -3.5 = -0.267354025 x = -0.267354025 Simplifying x = -0.267354025Subproblem 2
x + 3.5 = -3.232645975 Simplifying x + 3.5 = -3.232645975 Reorder the terms: 3.5 + x = -3.232645975 Solving 3.5 + x = -3.232645975 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 = -3.232645975 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -3.232645975 + -3.5 x = -3.232645975 + -3.5 Combine like terms: -3.232645975 + -3.5 = -6.732645975 x = -6.732645975 Simplifying x = -6.732645975Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.267354025, -6.732645975}Solution
x = {-0.267354025, -6.732645975}
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