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Simplifying 15x2 = 12x + 48 Reorder the terms: 15x2 = 48 + 12x Solving 15x2 = 48 + 12x Solving for variable 'x'. Reorder the terms: -48 + -12x + 15x2 = 48 + 12x + -48 + -12x Reorder the terms: -48 + -12x + 15x2 = 48 + -48 + 12x + -12x Combine like terms: 48 + -48 = 0 -48 + -12x + 15x2 = 0 + 12x + -12x -48 + -12x + 15x2 = 12x + -12x Combine like terms: 12x + -12x = 0 -48 + -12x + 15x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-16 + -4x + 5x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-16 + -4x + 5x2)' equal to zero and attempt to solve: Simplifying -16 + -4x + 5x2 = 0 Solving -16 + -4x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -3.2 + -0.8x + x2 = 0 Move the constant term to the right: Add '3.2' to each side of the equation. -3.2 + -0.8x + 3.2 + x2 = 0 + 3.2 Reorder the terms: -3.2 + 3.2 + -0.8x + x2 = 0 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + -0.8x + x2 = 0 + 3.2 -0.8x + x2 = 0 + 3.2 Combine like terms: 0 + 3.2 = 3.2 -0.8x + x2 = 3.2 The x term is -0.8x. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8x + 0.16 + x2 = 3.2 + 0.16 Reorder the terms: 0.16 + -0.8x + x2 = 3.2 + 0.16 Combine like terms: 3.2 + 0.16 = 3.36 0.16 + -0.8x + x2 = 3.36 Factor a perfect square on the left side: (x + -0.4)(x + -0.4) = 3.36 Calculate the square root of the right side: 1.833030278 Break this problem into two subproblems by setting (x + -0.4) equal to 1.833030278 and -1.833030278.Subproblem 1
x + -0.4 = 1.833030278 Simplifying x + -0.4 = 1.833030278 Reorder the terms: -0.4 + x = 1.833030278 Solving -0.4 + x = 1.833030278 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = 1.833030278 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = 1.833030278 + 0.4 x = 1.833030278 + 0.4 Combine like terms: 1.833030278 + 0.4 = 2.233030278 x = 2.233030278 Simplifying x = 2.233030278Subproblem 2
x + -0.4 = -1.833030278 Simplifying x + -0.4 = -1.833030278 Reorder the terms: -0.4 + x = -1.833030278 Solving -0.4 + x = -1.833030278 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = -1.833030278 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = -1.833030278 + 0.4 x = -1.833030278 + 0.4 Combine like terms: -1.833030278 + 0.4 = -1.433030278 x = -1.433030278 Simplifying x = -1.433030278Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.233030278, -1.433030278}Solution
x = {2.233030278, -1.433030278}
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