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Simplifying -12x(5x + -15) = 9x + 47 Reorder the terms: -12x(-15 + 5x) = 9x + 47 (-15 * -12x + 5x * -12x) = 9x + 47 (180x + -60x2) = 9x + 47 Reorder the terms: 180x + -60x2 = 47 + 9x Solving 180x + -60x2 = 47 + 9x Solving for variable 'x'. Reorder the terms: -47 + 180x + -9x + -60x2 = 47 + 9x + -47 + -9x Combine like terms: 180x + -9x = 171x -47 + 171x + -60x2 = 47 + 9x + -47 + -9x Reorder the terms: -47 + 171x + -60x2 = 47 + -47 + 9x + -9x Combine like terms: 47 + -47 = 0 -47 + 171x + -60x2 = 0 + 9x + -9x -47 + 171x + -60x2 = 9x + -9x Combine like terms: 9x + -9x = 0 -47 + 171x + -60x2 = 0 Begin completing the square. Divide all terms by -60 the coefficient of the squared term: Divide each side by '-60'. 0.7833333333 + -2.85x + x2 = 0.0 Move the constant term to the right: Add '-0.7833333333' to each side of the equation. 0.7833333333 + -2.85x + -0.7833333333 + x2 = 0.0 + -0.7833333333 Reorder the terms: 0.7833333333 + -0.7833333333 + -2.85x + x2 = 0.0 + -0.7833333333 Combine like terms: 0.7833333333 + -0.7833333333 = 0.0000000000 0.0000000000 + -2.85x + x2 = 0.0 + -0.7833333333 -2.85x + x2 = 0.0 + -0.7833333333 Combine like terms: 0.0 + -0.7833333333 = -0.7833333333 -2.85x + x2 = -0.7833333333 The x term is -2.85x. Take half its coefficient (-1.425). Square it (2.030625) and add it to both sides. Add '2.030625' to each side of the equation. -2.85x + 2.030625 + x2 = -0.7833333333 + 2.030625 Reorder the terms: 2.030625 + -2.85x + x2 = -0.7833333333 + 2.030625 Combine like terms: -0.7833333333 + 2.030625 = 1.2472916667 2.030625 + -2.85x + x2 = 1.2472916667 Factor a perfect square on the left side: (x + -1.425)(x + -1.425) = 1.2472916667 Calculate the square root of the right side: 1.116822128 Break this problem into two subproblems by setting (x + -1.425) equal to 1.116822128 and -1.116822128.Subproblem 1
x + -1.425 = 1.116822128 Simplifying x + -1.425 = 1.116822128 Reorder the terms: -1.425 + x = 1.116822128 Solving -1.425 + x = 1.116822128 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.425' to each side of the equation. -1.425 + 1.425 + x = 1.116822128 + 1.425 Combine like terms: -1.425 + 1.425 = 0.000 0.000 + x = 1.116822128 + 1.425 x = 1.116822128 + 1.425 Combine like terms: 1.116822128 + 1.425 = 2.541822128 x = 2.541822128 Simplifying x = 2.541822128Subproblem 2
x + -1.425 = -1.116822128 Simplifying x + -1.425 = -1.116822128 Reorder the terms: -1.425 + x = -1.116822128 Solving -1.425 + x = -1.116822128 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.425' to each side of the equation. -1.425 + 1.425 + x = -1.116822128 + 1.425 Combine like terms: -1.425 + 1.425 = 0.000 0.000 + x = -1.116822128 + 1.425 x = -1.116822128 + 1.425 Combine like terms: -1.116822128 + 1.425 = 0.308177872 x = 0.308177872 Simplifying x = 0.308177872Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.541822128, 0.308177872}
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