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Simplifying (5x + -3)(8x + -9) = 131 Reorder the terms: (-3 + 5x)(8x + -9) = 131 Reorder the terms: (-3 + 5x)(-9 + 8x) = 131 Multiply (-3 + 5x) * (-9 + 8x) (-3(-9 + 8x) + 5x * (-9 + 8x)) = 131 ((-9 * -3 + 8x * -3) + 5x * (-9 + 8x)) = 131 ((27 + -24x) + 5x * (-9 + 8x)) = 131 (27 + -24x + (-9 * 5x + 8x * 5x)) = 131 (27 + -24x + (-45x + 40x2)) = 131 Combine like terms: -24x + -45x = -69x (27 + -69x + 40x2) = 131 Solving 27 + -69x + 40x2 = 131 Solving for variable 'x'. Reorder the terms: 27 + -131 + -69x + 40x2 = 131 + -131 Combine like terms: 27 + -131 = -104 -104 + -69x + 40x2 = 131 + -131 Combine like terms: 131 + -131 = 0 -104 + -69x + 40x2 = 0 Begin completing the square. Divide all terms by 40 the coefficient of the squared term: Divide each side by '40'. -2.6 + -1.725x + x2 = 0.0 Move the constant term to the right: Add '2.6' to each side of the equation. -2.6 + -1.725x + 2.6 + x2 = 0.0 + 2.6 Reorder the terms: -2.6 + 2.6 + -1.725x + x2 = 0.0 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + -1.725x + x2 = 0.0 + 2.6 -1.725x + x2 = 0.0 + 2.6 Combine like terms: 0.0 + 2.6 = 2.6 -1.725x + x2 = 2.6 The x term is -1.725x. Take half its coefficient (-0.8625). Square it (0.74390625) and add it to both sides. Add '0.74390625' to each side of the equation. -1.725x + 0.74390625 + x2 = 2.6 + 0.74390625 Reorder the terms: 0.74390625 + -1.725x + x2 = 2.6 + 0.74390625 Combine like terms: 2.6 + 0.74390625 = 3.34390625 0.74390625 + -1.725x + x2 = 3.34390625 Factor a perfect square on the left side: (x + -0.8625)(x + -0.8625) = 3.34390625 Calculate the square root of the right side: 1.828635078 Break this problem into two subproblems by setting (x + -0.8625) equal to 1.828635078 and -1.828635078.Subproblem 1
x + -0.8625 = 1.828635078 Simplifying x + -0.8625 = 1.828635078 Reorder the terms: -0.8625 + x = 1.828635078 Solving -0.8625 + x = 1.828635078 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8625' to each side of the equation. -0.8625 + 0.8625 + x = 1.828635078 + 0.8625 Combine like terms: -0.8625 + 0.8625 = 0.0000 0.0000 + x = 1.828635078 + 0.8625 x = 1.828635078 + 0.8625 Combine like terms: 1.828635078 + 0.8625 = 2.691135078 x = 2.691135078 Simplifying x = 2.691135078Subproblem 2
x + -0.8625 = -1.828635078 Simplifying x + -0.8625 = -1.828635078 Reorder the terms: -0.8625 + x = -1.828635078 Solving -0.8625 + x = -1.828635078 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8625' to each side of the equation. -0.8625 + 0.8625 + x = -1.828635078 + 0.8625 Combine like terms: -0.8625 + 0.8625 = 0.0000 0.0000 + x = -1.828635078 + 0.8625 x = -1.828635078 + 0.8625 Combine like terms: -1.828635078 + 0.8625 = -0.966135078 x = -0.966135078 Simplifying x = -0.966135078Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.691135078, -0.966135078}
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