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Simplifying 50 + 30x = 2x2 Solving 50 + 30x = 2x2 Solving for variable 'x'. Combine like terms: 2x2 + -2x2 = 0 50 + 30x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(25 + 15x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(25 + 15x + -1x2)' equal to zero and attempt to solve: Simplifying 25 + 15x + -1x2 = 0 Solving 25 + 15x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -25 + -15x + x2 = 0 Move the constant term to the right: Add '25' to each side of the equation. -25 + -15x + 25 + x2 = 0 + 25 Reorder the terms: -25 + 25 + -15x + x2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -15x + x2 = 0 + 25 -15x + x2 = 0 + 25 Combine like terms: 0 + 25 = 25 -15x + x2 = 25 The x term is -15x. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15x + 56.25 + x2 = 25 + 56.25 Reorder the terms: 56.25 + -15x + x2 = 25 + 56.25 Combine like terms: 25 + 56.25 = 81.25 56.25 + -15x + x2 = 81.25 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 81.25 Calculate the square root of the right side: 9.013878189 Break this problem into two subproblems by setting (x + -7.5) equal to 9.013878189 and -9.013878189.Subproblem 1
x + -7.5 = 9.013878189 Simplifying x + -7.5 = 9.013878189 Reorder the terms: -7.5 + x = 9.013878189 Solving -7.5 + x = 9.013878189 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = 9.013878189 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 9.013878189 + 7.5 x = 9.013878189 + 7.5 Combine like terms: 9.013878189 + 7.5 = 16.513878189 x = 16.513878189 Simplifying x = 16.513878189Subproblem 2
x + -7.5 = -9.013878189 Simplifying x + -7.5 = -9.013878189 Reorder the terms: -7.5 + x = -9.013878189 Solving -7.5 + x = -9.013878189 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = -9.013878189 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -9.013878189 + 7.5 x = -9.013878189 + 7.5 Combine like terms: -9.013878189 + 7.5 = -1.513878189 x = -1.513878189 Simplifying x = -1.513878189Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.513878189, -1.513878189}Solution
x = {16.513878189, -1.513878189}
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