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Simplifying 5(3x + -2) * 6x = 1 Reorder the terms: 5(-2 + 3x) * 6x = 1 Reorder the terms for easier multiplication: 5 * 6x(-2 + 3x) = 1 Multiply 5 * 6 30x(-2 + 3x) = 1 (-2 * 30x + 3x * 30x) = 1 (-60x + 90x2) = 1 Solving -60x + 90x2 = 1 Solving for variable 'x'. Reorder the terms: -1 + -60x + 90x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + -60x + 90x2 = 0 Begin completing the square. Divide all terms by 90 the coefficient of the squared term: Divide each side by '90'. -0.01111111111 + -0.6666666667x + x2 = 0.0 Move the constant term to the right: Add '0.01111111111' to each side of the equation. -0.01111111111 + -0.6666666667x + 0.01111111111 + x2 = 0.0 + 0.01111111111 Reorder the terms: -0.01111111111 + 0.01111111111 + -0.6666666667x + x2 = 0.0 + 0.01111111111 Combine like terms: -0.01111111111 + 0.01111111111 = 0.00000000000 0.00000000000 + -0.6666666667x + x2 = 0.0 + 0.01111111111 -0.6666666667x + x2 = 0.0 + 0.01111111111 Combine like terms: 0.0 + 0.01111111111 = 0.01111111111 -0.6666666667x + x2 = 0.01111111111 The x term is -0.6666666667x. Take half its coefficient (-0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. -0.6666666667x + 0.1111111112 + x2 = 0.01111111111 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667x + x2 = 0.01111111111 + 0.1111111112 Combine like terms: 0.01111111111 + 0.1111111112 = 0.12222222231 0.1111111112 + -0.6666666667x + x2 = 0.12222222231 Factor a perfect square on the left side: (x + -0.3333333334)(x + -0.3333333334) = 0.12222222231 Calculate the square root of the right side: 0.34960295 Break this problem into two subproblems by setting (x + -0.3333333334) equal to 0.34960295 and -0.34960295.Subproblem 1
x + -0.3333333334 = 0.34960295 Simplifying x + -0.3333333334 = 0.34960295 Reorder the terms: -0.3333333334 + x = 0.34960295 Solving -0.3333333334 + x = 0.34960295 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + x = 0.34960295 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = 0.34960295 + 0.3333333334 x = 0.34960295 + 0.3333333334 Combine like terms: 0.34960295 + 0.3333333334 = 0.6829362834 x = 0.6829362834 Simplifying x = 0.6829362834Subproblem 2
x + -0.3333333334 = -0.34960295 Simplifying x + -0.3333333334 = -0.34960295 Reorder the terms: -0.3333333334 + x = -0.34960295 Solving -0.3333333334 + x = -0.34960295 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + x = -0.34960295 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = -0.34960295 + 0.3333333334 x = -0.34960295 + 0.3333333334 Combine like terms: -0.34960295 + 0.3333333334 = -0.0162696166 x = -0.0162696166 Simplifying x = -0.0162696166Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6829362834, -0.0162696166}
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