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Simplifying (0.012x + -0.17)(0.3x + 0.54) = 0 Reorder the terms: (-0.17 + 0.012x)(0.3x + 0.54) = 0 Reorder the terms: (-0.17 + 0.012x)(0.54 + 0.3x) = 0 Multiply (-0.17 + 0.012x) * (0.54 + 0.3x) (-0.17(0.54 + 0.3x) + 0.012x * (0.54 + 0.3x)) = 0 ((0.54 * -0.17 + 0.3x * -0.17) + 0.012x * (0.54 + 0.3x)) = 0 ((-0.0918 + -0.051x) + 0.012x * (0.54 + 0.3x)) = 0 (-0.0918 + -0.051x + (0.54 * 0.012x + 0.3x * 0.012x)) = 0 (-0.0918 + -0.051x + (0.00648x + 0.0036x2)) = 0 Combine like terms: -0.051x + 0.00648x = -0.04452x (-0.0918 + -0.04452x + 0.0036x2) = 0 Solving -0.0918 + -0.04452x + 0.0036x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.0036 the coefficient of the squared term: Divide each side by '0.0036'. -25.5 + -12.36666667x + x2 = 0 Move the constant term to the right: Add '25.5' to each side of the equation. -25.5 + -12.36666667x + 25.5 + x2 = 0 + 25.5 Reorder the terms: -25.5 + 25.5 + -12.36666667x + x2 = 0 + 25.5 Combine like terms: -25.5 + 25.5 = 0.0 0.0 + -12.36666667x + x2 = 0 + 25.5 -12.36666667x + x2 = 0 + 25.5 Combine like terms: 0 + 25.5 = 25.5 -12.36666667x + x2 = 25.5 The x term is -12.36666667x. Take half its coefficient (-6.183333335). Square it (38.23361113) and add it to both sides. Add '38.23361113' to each side of the equation. -12.36666667x + 38.23361113 + x2 = 25.5 + 38.23361113 Reorder the terms: 38.23361113 + -12.36666667x + x2 = 25.5 + 38.23361113 Combine like terms: 25.5 + 38.23361113 = 63.73361113 38.23361113 + -12.36666667x + x2 = 63.73361113 Factor a perfect square on the left side: (x + -6.183333335)(x + -6.183333335) = 63.73361113 Calculate the square root of the right side: 7.983333335 Break this problem into two subproblems by setting (x + -6.183333335) equal to 7.983333335 and -7.983333335.Subproblem 1
x + -6.183333335 = 7.983333335 Simplifying x + -6.183333335 = 7.983333335 Reorder the terms: -6.183333335 + x = 7.983333335 Solving -6.183333335 + x = 7.983333335 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.183333335' to each side of the equation. -6.183333335 + 6.183333335 + x = 7.983333335 + 6.183333335 Combine like terms: -6.183333335 + 6.183333335 = 0.000000000 0.000000000 + x = 7.983333335 + 6.183333335 x = 7.983333335 + 6.183333335 Combine like terms: 7.983333335 + 6.183333335 = 14.16666667 x = 14.16666667 Simplifying x = 14.16666667Subproblem 2
x + -6.183333335 = -7.983333335 Simplifying x + -6.183333335 = -7.983333335 Reorder the terms: -6.183333335 + x = -7.983333335 Solving -6.183333335 + x = -7.983333335 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.183333335' to each side of the equation. -6.183333335 + 6.183333335 + x = -7.983333335 + 6.183333335 Combine like terms: -6.183333335 + 6.183333335 = 0.000000000 0.000000000 + x = -7.983333335 + 6.183333335 x = -7.983333335 + 6.183333335 Combine like terms: -7.983333335 + 6.183333335 = -1.8 x = -1.8 Simplifying x = -1.8Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.16666667, -1.8}
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