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Simplifying 30x + 30 = 4x2 + 16 Reorder the terms: 30 + 30x = 4x2 + 16 Reorder the terms: 30 + 30x = 16 + 4x2 Solving 30 + 30x = 16 + 4x2 Solving for variable 'x'. Reorder the terms: 30 + -16 + 30x + -4x2 = 16 + 4x2 + -16 + -4x2 Combine like terms: 30 + -16 = 14 14 + 30x + -4x2 = 16 + 4x2 + -16 + -4x2 Reorder the terms: 14 + 30x + -4x2 = 16 + -16 + 4x2 + -4x2 Combine like terms: 16 + -16 = 0 14 + 30x + -4x2 = 0 + 4x2 + -4x2 14 + 30x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 14 + 30x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(7 + 15x + -2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7 + 15x + -2x2)' equal to zero and attempt to solve: Simplifying 7 + 15x + -2x2 = 0 Solving 7 + 15x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -3.5 + -7.5x + x2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + -7.5x + 3.5 + x2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + -7.5x + x2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + -7.5x + x2 = 0 + 3.5 -7.5x + x2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 -7.5x + x2 = 3.5 The x term is -7.5x. Take half its coefficient (-3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. -7.5x + 14.0625 + x2 = 3.5 + 14.0625 Reorder the terms: 14.0625 + -7.5x + x2 = 3.5 + 14.0625 Combine like terms: 3.5 + 14.0625 = 17.5625 14.0625 + -7.5x + x2 = 17.5625 Factor a perfect square on the left side: (x + -3.75)(x + -3.75) = 17.5625 Calculate the square root of the right side: 4.190763654 Break this problem into two subproblems by setting (x + -3.75) equal to 4.190763654 and -4.190763654.Subproblem 1
x + -3.75 = 4.190763654 Simplifying x + -3.75 = 4.190763654 Reorder the terms: -3.75 + x = 4.190763654 Solving -3.75 + x = 4.190763654 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x = 4.190763654 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = 4.190763654 + 3.75 x = 4.190763654 + 3.75 Combine like terms: 4.190763654 + 3.75 = 7.940763654 x = 7.940763654 Simplifying x = 7.940763654Subproblem 2
x + -3.75 = -4.190763654 Simplifying x + -3.75 = -4.190763654 Reorder the terms: -3.75 + x = -4.190763654 Solving -3.75 + x = -4.190763654 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x = -4.190763654 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = -4.190763654 + 3.75 x = -4.190763654 + 3.75 Combine like terms: -4.190763654 + 3.75 = -0.440763654 x = -0.440763654 Simplifying x = -0.440763654Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.940763654, -0.440763654}Solution
x = {7.940763654, -0.440763654}
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