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Simplifying 2x2 + -12x2 = 32x + -192 Combine like terms: 2x2 + -12x2 = -10x2 -10x2 = 32x + -192 Reorder the terms: -10x2 = -192 + 32x Solving -10x2 = -192 + 32x Solving for variable 'x'. Reorder the terms: 192 + -32x + -10x2 = -192 + 32x + 192 + -32x Reorder the terms: 192 + -32x + -10x2 = -192 + 192 + 32x + -32x Combine like terms: -192 + 192 = 0 192 + -32x + -10x2 = 0 + 32x + -32x 192 + -32x + -10x2 = 32x + -32x Combine like terms: 32x + -32x = 0 192 + -32x + -10x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(96 + -16x + -5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(96 + -16x + -5x2)' equal to zero and attempt to solve: Simplifying 96 + -16x + -5x2 = 0 Solving 96 + -16x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -19.2 + 3.2x + x2 = 0 Move the constant term to the right: Add '19.2' to each side of the equation. -19.2 + 3.2x + 19.2 + x2 = 0 + 19.2 Reorder the terms: -19.2 + 19.2 + 3.2x + x2 = 0 + 19.2 Combine like terms: -19.2 + 19.2 = 0.0 0.0 + 3.2x + x2 = 0 + 19.2 3.2x + x2 = 0 + 19.2 Combine like terms: 0 + 19.2 = 19.2 3.2x + x2 = 19.2 The x term is 3.2x. Take half its coefficient (1.6). Square it (2.56) and add it to both sides. Add '2.56' to each side of the equation. 3.2x + 2.56 + x2 = 19.2 + 2.56 Reorder the terms: 2.56 + 3.2x + x2 = 19.2 + 2.56 Combine like terms: 19.2 + 2.56 = 21.76 2.56 + 3.2x + x2 = 21.76 Factor a perfect square on the left side: (x + 1.6)(x + 1.6) = 21.76 Calculate the square root of the right side: 4.664761516 Break this problem into two subproblems by setting (x + 1.6) equal to 4.664761516 and -4.664761516.Subproblem 1
x + 1.6 = 4.664761516 Simplifying x + 1.6 = 4.664761516 Reorder the terms: 1.6 + x = 4.664761516 Solving 1.6 + x = 4.664761516 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.6' to each side of the equation. 1.6 + -1.6 + x = 4.664761516 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + x = 4.664761516 + -1.6 x = 4.664761516 + -1.6 Combine like terms: 4.664761516 + -1.6 = 3.064761516 x = 3.064761516 Simplifying x = 3.064761516Subproblem 2
x + 1.6 = -4.664761516 Simplifying x + 1.6 = -4.664761516 Reorder the terms: 1.6 + x = -4.664761516 Solving 1.6 + x = -4.664761516 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.6' to each side of the equation. 1.6 + -1.6 + x = -4.664761516 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + x = -4.664761516 + -1.6 x = -4.664761516 + -1.6 Combine like terms: -4.664761516 + -1.6 = -6.264761516 x = -6.264761516 Simplifying x = -6.264761516Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.064761516, -6.264761516}Solution
x = {3.064761516, -6.264761516}
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