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Simplifying 22x2 + -1320x + -3190 = 0 Reorder the terms: -3190 + -1320x + 22x2 = 0 Solving -3190 + -1320x + 22x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '22'. 22(-145 + -60x + x2) = 0 Ignore the factor 22.Subproblem 1
Set the factor '(-145 + -60x + x2)' equal to zero and attempt to solve: Simplifying -145 + -60x + x2 = 0 Solving -145 + -60x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '145' to each side of the equation. -145 + -60x + 145 + x2 = 0 + 145 Reorder the terms: -145 + 145 + -60x + x2 = 0 + 145 Combine like terms: -145 + 145 = 0 0 + -60x + x2 = 0 + 145 -60x + x2 = 0 + 145 Combine like terms: 0 + 145 = 145 -60x + x2 = 145 The x term is -60x. Take half its coefficient (-30). Square it (900) and add it to both sides. Add '900' to each side of the equation. -60x + 900 + x2 = 145 + 900 Reorder the terms: 900 + -60x + x2 = 145 + 900 Combine like terms: 145 + 900 = 1045 900 + -60x + x2 = 1045 Factor a perfect square on the left side: (x + -30)(x + -30) = 1045 Calculate the square root of the right side: 32.32645975 Break this problem into two subproblems by setting (x + -30) equal to 32.32645975 and -32.32645975.Subproblem 1
x + -30 = 32.32645975 Simplifying x + -30 = 32.32645975 Reorder the terms: -30 + x = 32.32645975 Solving -30 + x = 32.32645975 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + x = 32.32645975 + 30 Combine like terms: -30 + 30 = 0 0 + x = 32.32645975 + 30 x = 32.32645975 + 30 Combine like terms: 32.32645975 + 30 = 62.32645975 x = 62.32645975 Simplifying x = 62.32645975Subproblem 2
x + -30 = -32.32645975 Simplifying x + -30 = -32.32645975 Reorder the terms: -30 + x = -32.32645975 Solving -30 + x = -32.32645975 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + x = -32.32645975 + 30 Combine like terms: -30 + 30 = 0 0 + x = -32.32645975 + 30 x = -32.32645975 + 30 Combine like terms: -32.32645975 + 30 = -2.32645975 x = -2.32645975 Simplifying x = -2.32645975Solution
The solution to the problem is based on the solutions from the subproblems. x = {62.32645975, -2.32645975}Solution
x = {62.32645975, -2.32645975}
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