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Simplifying 30 = 48x + -16x2 Solving 30 = 48x + -16x2 Solving for variable 'x'. Reorder the terms: 30 + -48x + 16x2 = 48x + -48x + -16x2 + 16x2 Combine like terms: 48x + -48x = 0 30 + -48x + 16x2 = 0 + -16x2 + 16x2 30 + -48x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 30 + -48x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(15 + -24x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(15 + -24x + 8x2)' equal to zero and attempt to solve: Simplifying 15 + -24x + 8x2 = 0 Solving 15 + -24x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 1.875 + -3x + x2 = 0 Move the constant term to the right: Add '-1.875' to each side of the equation. 1.875 + -3x + -1.875 + x2 = 0 + -1.875 Reorder the terms: 1.875 + -1.875 + -3x + x2 = 0 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + -3x + x2 = 0 + -1.875 -3x + x2 = 0 + -1.875 Combine like terms: 0 + -1.875 = -1.875 -3x + x2 = -1.875 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = -1.875 + 2.25 Reorder the terms: 2.25 + -3x + x2 = -1.875 + 2.25 Combine like terms: -1.875 + 2.25 = 0.375 2.25 + -3x + x2 = 0.375 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 0.375 Calculate the square root of the right side: 0.612372436 Break this problem into two subproblems by setting (x + -1.5) equal to 0.612372436 and -0.612372436.Subproblem 1
x + -1.5 = 0.612372436 Simplifying x + -1.5 = 0.612372436 Reorder the terms: -1.5 + x = 0.612372436 Solving -1.5 + x = 0.612372436 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 0.612372436 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 0.612372436 + 1.5 x = 0.612372436 + 1.5 Combine like terms: 0.612372436 + 1.5 = 2.112372436 x = 2.112372436 Simplifying x = 2.112372436Subproblem 2
x + -1.5 = -0.612372436 Simplifying x + -1.5 = -0.612372436 Reorder the terms: -1.5 + x = -0.612372436 Solving -1.5 + x = -0.612372436 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -0.612372436 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -0.612372436 + 1.5 x = -0.612372436 + 1.5 Combine like terms: -0.612372436 + 1.5 = 0.887627564 x = 0.887627564 Simplifying x = 0.887627564Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.112372436, 0.887627564}Solution
x = {2.112372436, 0.887627564}
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