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Simplifying 3x2 + 147 = 48x Reorder the terms: 147 + 3x2 = 48x Solving 147 + 3x2 = 48x Solving for variable 'x'. Reorder the terms: 147 + -48x + 3x2 = 48x + -48x Combine like terms: 48x + -48x = 0 147 + -48x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(49 + -16x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(49 + -16x + x2)' equal to zero and attempt to solve: Simplifying 49 + -16x + x2 = 0 Solving 49 + -16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-49' to each side of the equation. 49 + -16x + -49 + x2 = 0 + -49 Reorder the terms: 49 + -49 + -16x + x2 = 0 + -49 Combine like terms: 49 + -49 = 0 0 + -16x + x2 = 0 + -49 -16x + x2 = 0 + -49 Combine like terms: 0 + -49 = -49 -16x + x2 = -49 The x term is -16x. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16x + 64 + x2 = -49 + 64 Reorder the terms: 64 + -16x + x2 = -49 + 64 Combine like terms: -49 + 64 = 15 64 + -16x + x2 = 15 Factor a perfect square on the left side: (x + -8)(x + -8) = 15 Calculate the square root of the right side: 3.872983346 Break this problem into two subproblems by setting (x + -8) equal to 3.872983346 and -3.872983346.Subproblem 1
x + -8 = 3.872983346 Simplifying x + -8 = 3.872983346 Reorder the terms: -8 + x = 3.872983346 Solving -8 + x = 3.872983346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 3.872983346 + 8 Combine like terms: -8 + 8 = 0 0 + x = 3.872983346 + 8 x = 3.872983346 + 8 Combine like terms: 3.872983346 + 8 = 11.872983346 x = 11.872983346 Simplifying x = 11.872983346Subproblem 2
x + -8 = -3.872983346 Simplifying x + -8 = -3.872983346 Reorder the terms: -8 + x = -3.872983346 Solving -8 + x = -3.872983346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = -3.872983346 + 8 Combine like terms: -8 + 8 = 0 0 + x = -3.872983346 + 8 x = -3.872983346 + 8 Combine like terms: -3.872983346 + 8 = 4.127016654 x = 4.127016654 Simplifying x = 4.127016654Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.872983346, 4.127016654}Solution
x = {11.872983346, 4.127016654}
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