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Simplifying 3x + 4x(4x + 24) = 360 Reorder the terms: 3x + 4x(24 + 4x) = 360 3x + (24 * 4x + 4x * 4x) = 360 3x + (96x + 16x2) = 360 Combine like terms: 3x + 96x = 99x 99x + 16x2 = 360 Solving 99x + 16x2 = 360 Solving for variable 'x'. Reorder the terms: -360 + 99x + 16x2 = 360 + -360 Combine like terms: 360 + -360 = 0 -360 + 99x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -22.5 + 6.1875x + x2 = 0 Move the constant term to the right: Add '22.5' to each side of the equation. -22.5 + 6.1875x + 22.5 + x2 = 0 + 22.5 Reorder the terms: -22.5 + 22.5 + 6.1875x + x2 = 0 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + 6.1875x + x2 = 0 + 22.5 6.1875x + x2 = 0 + 22.5 Combine like terms: 0 + 22.5 = 22.5 6.1875x + x2 = 22.5 The x term is 6.1875x. Take half its coefficient (3.09375). Square it (9.571289063) and add it to both sides. Add '9.571289063' to each side of the equation. 6.1875x + 9.571289063 + x2 = 22.5 + 9.571289063 Reorder the terms: 9.571289063 + 6.1875x + x2 = 22.5 + 9.571289063 Combine like terms: 22.5 + 9.571289063 = 32.071289063 9.571289063 + 6.1875x + x2 = 32.071289063 Factor a perfect square on the left side: (x + 3.09375)(x + 3.09375) = 32.071289063 Calculate the square root of the right side: 5.663151866 Break this problem into two subproblems by setting (x + 3.09375) equal to 5.663151866 and -5.663151866.Subproblem 1
x + 3.09375 = 5.663151866 Simplifying x + 3.09375 = 5.663151866 Reorder the terms: 3.09375 + x = 5.663151866 Solving 3.09375 + x = 5.663151866 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.09375' to each side of the equation. 3.09375 + -3.09375 + x = 5.663151866 + -3.09375 Combine like terms: 3.09375 + -3.09375 = 0.00000 0.00000 + x = 5.663151866 + -3.09375 x = 5.663151866 + -3.09375 Combine like terms: 5.663151866 + -3.09375 = 2.569401866 x = 2.569401866 Simplifying x = 2.569401866Subproblem 2
x + 3.09375 = -5.663151866 Simplifying x + 3.09375 = -5.663151866 Reorder the terms: 3.09375 + x = -5.663151866 Solving 3.09375 + x = -5.663151866 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.09375' to each side of the equation. 3.09375 + -3.09375 + x = -5.663151866 + -3.09375 Combine like terms: 3.09375 + -3.09375 = 0.00000 0.00000 + x = -5.663151866 + -3.09375 x = -5.663151866 + -3.09375 Combine like terms: -5.663151866 + -3.09375 = -8.756901866 x = -8.756901866 Simplifying x = -8.756901866Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.569401866, -8.756901866}
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