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Simplifying (2x + -7.8)(9x + -12.6) = 0 Reorder the terms: (-7.8 + 2x)(9x + -12.6) = 0 Reorder the terms: (-7.8 + 2x)(-12.6 + 9x) = 0 Multiply (-7.8 + 2x) * (-12.6 + 9x) (-7.8(-12.6 + 9x) + 2x * (-12.6 + 9x)) = 0 ((-12.6 * -7.8 + 9x * -7.8) + 2x * (-12.6 + 9x)) = 0 ((98.28 + -70.2x) + 2x * (-12.6 + 9x)) = 0 (98.28 + -70.2x + (-12.6 * 2x + 9x * 2x)) = 0 (98.28 + -70.2x + (-25.2x + 18x2)) = 0 Combine like terms: -70.2x + -25.2x = -95.4x (98.28 + -95.4x + 18x2) = 0 Solving 98.28 + -95.4x + 18x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. 5.46 + -5.3x + x2 = 0 Move the constant term to the right: Add '-5.46' to each side of the equation. 5.46 + -5.3x + -5.46 + x2 = 0 + -5.46 Reorder the terms: 5.46 + -5.46 + -5.3x + x2 = 0 + -5.46 Combine like terms: 5.46 + -5.46 = 0.00 0.00 + -5.3x + x2 = 0 + -5.46 -5.3x + x2 = 0 + -5.46 Combine like terms: 0 + -5.46 = -5.46 -5.3x + x2 = -5.46 The x term is -5.3x. Take half its coefficient (-2.65). Square it (7.0225) and add it to both sides. Add '7.0225' to each side of the equation. -5.3x + 7.0225 + x2 = -5.46 + 7.0225 Reorder the terms: 7.0225 + -5.3x + x2 = -5.46 + 7.0225 Combine like terms: -5.46 + 7.0225 = 1.5625 7.0225 + -5.3x + x2 = 1.5625 Factor a perfect square on the left side: (x + -2.65)(x + -2.65) = 1.5625 Calculate the square root of the right side: 1.25 Break this problem into two subproblems by setting (x + -2.65) equal to 1.25 and -1.25.Subproblem 1
x + -2.65 = 1.25 Simplifying x + -2.65 = 1.25 Reorder the terms: -2.65 + x = 1.25 Solving -2.65 + x = 1.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.65' to each side of the equation. -2.65 + 2.65 + x = 1.25 + 2.65 Combine like terms: -2.65 + 2.65 = 0.00 0.00 + x = 1.25 + 2.65 x = 1.25 + 2.65 Combine like terms: 1.25 + 2.65 = 3.9 x = 3.9 Simplifying x = 3.9Subproblem 2
x + -2.65 = -1.25 Simplifying x + -2.65 = -1.25 Reorder the terms: -2.65 + x = -1.25 Solving -2.65 + x = -1.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.65' to each side of the equation. -2.65 + 2.65 + x = -1.25 + 2.65 Combine like terms: -2.65 + 2.65 = 0.00 0.00 + x = -1.25 + 2.65 x = -1.25 + 2.65 Combine like terms: -1.25 + 2.65 = 1.4 x = 1.4 Simplifying x = 1.4Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.9, 1.4}
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