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Simplifying 5x(x + -18) = 6 + -2(x + 15) Reorder the terms: 5x(-18 + x) = 6 + -2(x + 15) (-18 * 5x + x * 5x) = 6 + -2(x + 15) (-90x + 5x2) = 6 + -2(x + 15) Reorder the terms: -90x + 5x2 = 6 + -2(15 + x) -90x + 5x2 = 6 + (15 * -2 + x * -2) -90x + 5x2 = 6 + (-30 + -2x) Combine like terms: 6 + -30 = -24 -90x + 5x2 = -24 + -2x Solving -90x + 5x2 = -24 + -2x Solving for variable 'x'. Reorder the terms: 24 + -90x + 2x + 5x2 = -24 + -2x + 24 + 2x Combine like terms: -90x + 2x = -88x 24 + -88x + 5x2 = -24 + -2x + 24 + 2x Reorder the terms: 24 + -88x + 5x2 = -24 + 24 + -2x + 2x Combine like terms: -24 + 24 = 0 24 + -88x + 5x2 = 0 + -2x + 2x 24 + -88x + 5x2 = -2x + 2x Combine like terms: -2x + 2x = 0 24 + -88x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 4.8 + -17.6x + x2 = 0 Move the constant term to the right: Add '-4.8' to each side of the equation. 4.8 + -17.6x + -4.8 + x2 = 0 + -4.8 Reorder the terms: 4.8 + -4.8 + -17.6x + x2 = 0 + -4.8 Combine like terms: 4.8 + -4.8 = 0.0 0.0 + -17.6x + x2 = 0 + -4.8 -17.6x + x2 = 0 + -4.8 Combine like terms: 0 + -4.8 = -4.8 -17.6x + x2 = -4.8 The x term is -17.6x. Take half its coefficient (-8.8). Square it (77.44) and add it to both sides. Add '77.44' to each side of the equation. -17.6x + 77.44 + x2 = -4.8 + 77.44 Reorder the terms: 77.44 + -17.6x + x2 = -4.8 + 77.44 Combine like terms: -4.8 + 77.44 = 72.64 77.44 + -17.6x + x2 = 72.64 Factor a perfect square on the left side: (x + -8.8)(x + -8.8) = 72.64 Calculate the square root of the right side: 8.522910301 Break this problem into two subproblems by setting (x + -8.8) equal to 8.522910301 and -8.522910301.Subproblem 1
x + -8.8 = 8.522910301 Simplifying x + -8.8 = 8.522910301 Reorder the terms: -8.8 + x = 8.522910301 Solving -8.8 + x = 8.522910301 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.8' to each side of the equation. -8.8 + 8.8 + x = 8.522910301 + 8.8 Combine like terms: -8.8 + 8.8 = 0.0 0.0 + x = 8.522910301 + 8.8 x = 8.522910301 + 8.8 Combine like terms: 8.522910301 + 8.8 = 17.322910301 x = 17.322910301 Simplifying x = 17.322910301Subproblem 2
x + -8.8 = -8.522910301 Simplifying x + -8.8 = -8.522910301 Reorder the terms: -8.8 + x = -8.522910301 Solving -8.8 + x = -8.522910301 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.8' to each side of the equation. -8.8 + 8.8 + x = -8.522910301 + 8.8 Combine like terms: -8.8 + 8.8 = 0.0 0.0 + x = -8.522910301 + 8.8 x = -8.522910301 + 8.8 Combine like terms: -8.522910301 + 8.8 = 0.277089699 x = 0.277089699 Simplifying x = 0.277089699Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.322910301, 0.277089699}
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