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Simplifying 6 + -5(3 + -5(2 + -3x)) * x = 9 6 + -5(3 + (2 * -5 + -3x * -5)) * x = 9 6 + -5(3 + (-10 + 15x)) * x = 9 Combine like terms: 3 + -10 = -7 6 + -5(-7 + 15x) * x = 9 Reorder the terms for easier multiplication: 6 + -5x(-7 + 15x) = 9 6 + (-7 * -5x + 15x * -5x) = 9 6 + (35x + -75x2) = 9 Solving 6 + 35x + -75x2 = 9 Solving for variable 'x'. Reorder the terms: 6 + -9 + 35x + -75x2 = 9 + -9 Combine like terms: 6 + -9 = -3 -3 + 35x + -75x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -3 + 35x + -75x2 = 0 Begin completing the square. Divide all terms by -75 the coefficient of the squared term: Divide each side by '-75'. 0.04 + -0.4666666667x + x2 = 0 Move the constant term to the right: Add '-0.04' to each side of the equation. 0.04 + -0.4666666667x + -0.04 + x2 = 0 + -0.04 Reorder the terms: 0.04 + -0.04 + -0.4666666667x + x2 = 0 + -0.04 Combine like terms: 0.04 + -0.04 = 0.00 0.00 + -0.4666666667x + x2 = 0 + -0.04 -0.4666666667x + x2 = 0 + -0.04 Combine like terms: 0 + -0.04 = -0.04 -0.4666666667x + x2 = -0.04 The x term is -0.4666666667x. Take half its coefficient (-0.2333333334). Square it (0.05444444448) and add it to both sides. Add '0.05444444448' to each side of the equation. -0.4666666667x + 0.05444444448 + x2 = -0.04 + 0.05444444448 Reorder the terms: 0.05444444448 + -0.4666666667x + x2 = -0.04 + 0.05444444448 Combine like terms: -0.04 + 0.05444444448 = 0.01444444448 0.05444444448 + -0.4666666667x + x2 = 0.01444444448 Factor a perfect square on the left side: (x + -0.2333333334)(x + -0.2333333334) = 0.01444444448 Calculate the square root of the right side: 0.120185043 Break this problem into two subproblems by setting (x + -0.2333333334) equal to 0.120185043 and -0.120185043.Subproblem 1
x + -0.2333333334 = 0.120185043 Simplifying x + -0.2333333334 = 0.120185043 Reorder the terms: -0.2333333334 + x = 0.120185043 Solving -0.2333333334 + x = 0.120185043 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2333333334' to each side of the equation. -0.2333333334 + 0.2333333334 + x = 0.120185043 + 0.2333333334 Combine like terms: -0.2333333334 + 0.2333333334 = 0.0000000000 0.0000000000 + x = 0.120185043 + 0.2333333334 x = 0.120185043 + 0.2333333334 Combine like terms: 0.120185043 + 0.2333333334 = 0.3535183764 x = 0.3535183764 Simplifying x = 0.3535183764Subproblem 2
x + -0.2333333334 = -0.120185043 Simplifying x + -0.2333333334 = -0.120185043 Reorder the terms: -0.2333333334 + x = -0.120185043 Solving -0.2333333334 + x = -0.120185043 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2333333334' to each side of the equation. -0.2333333334 + 0.2333333334 + x = -0.120185043 + 0.2333333334 Combine like terms: -0.2333333334 + 0.2333333334 = 0.0000000000 0.0000000000 + x = -0.120185043 + 0.2333333334 x = -0.120185043 + 0.2333333334 Combine like terms: -0.120185043 + 0.2333333334 = 0.1131482904 x = 0.1131482904 Simplifying x = 0.1131482904Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3535183764, 0.1131482904}
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