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Simplifying (5x2 + -9x + 23) + -1(11x2 + -7) = 0 Reorder the terms: (23 + -9x + 5x2) + -1(11x2 + -7) = 0 Remove parenthesis around (23 + -9x + 5x2) 23 + -9x + 5x2 + -1(11x2 + -7) = 0 Reorder the terms: 23 + -9x + 5x2 + -1(-7 + 11x2) = 0 23 + -9x + 5x2 + (-7 * -1 + 11x2 * -1) = 0 23 + -9x + 5x2 + (7 + -11x2) = 0 Reorder the terms: 23 + 7 + -9x + 5x2 + -11x2 = 0 Combine like terms: 23 + 7 = 30 30 + -9x + 5x2 + -11x2 = 0 Combine like terms: 5x2 + -11x2 = -6x2 30 + -9x + -6x2 = 0 Solving 30 + -9x + -6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(10 + -3x + -2x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(10 + -3x + -2x2)' equal to zero and attempt to solve: Simplifying 10 + -3x + -2x2 = 0 Solving 10 + -3x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -5 + 1.5x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + 1.5x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + 1.5x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 1.5x + x2 = 0 + 5 1.5x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 1.5x + x2 = 5 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 5 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 5 + 0.5625 Combine like terms: 5 + 0.5625 = 5.5625 0.5625 + 1.5x + x2 = 5.5625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 5.5625 Calculate the square root of the right side: 2.358495283 Break this problem into two subproblems by setting (x + 0.75) equal to 2.358495283 and -2.358495283.Subproblem 1
x + 0.75 = 2.358495283 Simplifying x + 0.75 = 2.358495283 Reorder the terms: 0.75 + x = 2.358495283 Solving 0.75 + x = 2.358495283 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 2.358495283 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 2.358495283 + -0.75 x = 2.358495283 + -0.75 Combine like terms: 2.358495283 + -0.75 = 1.608495283 x = 1.608495283 Simplifying x = 1.608495283Subproblem 2
x + 0.75 = -2.358495283 Simplifying x + 0.75 = -2.358495283 Reorder the terms: 0.75 + x = -2.358495283 Solving 0.75 + x = -2.358495283 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -2.358495283 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -2.358495283 + -0.75 x = -2.358495283 + -0.75 Combine like terms: -2.358495283 + -0.75 = -3.108495283 x = -3.108495283 Simplifying x = -3.108495283Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.608495283, -3.108495283}Solution
x = {1.608495283, -3.108495283}
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