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Simplifying 3x2 + -84x + 153 = 0 Reorder the terms: 153 + -84x + 3x2 = 0 Solving 153 + -84x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(51 + -28x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(51 + -28x + x2)' equal to zero and attempt to solve: Simplifying 51 + -28x + x2 = 0 Solving 51 + -28x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-51' to each side of the equation. 51 + -28x + -51 + x2 = 0 + -51 Reorder the terms: 51 + -51 + -28x + x2 = 0 + -51 Combine like terms: 51 + -51 = 0 0 + -28x + x2 = 0 + -51 -28x + x2 = 0 + -51 Combine like terms: 0 + -51 = -51 -28x + x2 = -51 The x term is -28x. Take half its coefficient (-14). Square it (196) and add it to both sides. Add '196' to each side of the equation. -28x + 196 + x2 = -51 + 196 Reorder the terms: 196 + -28x + x2 = -51 + 196 Combine like terms: -51 + 196 = 145 196 + -28x + x2 = 145 Factor a perfect square on the left side: (x + -14)(x + -14) = 145 Calculate the square root of the right side: 12.041594579 Break this problem into two subproblems by setting (x + -14) equal to 12.041594579 and -12.041594579.Subproblem 1
x + -14 = 12.041594579 Simplifying x + -14 = 12.041594579 Reorder the terms: -14 + x = 12.041594579 Solving -14 + x = 12.041594579 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + x = 12.041594579 + 14 Combine like terms: -14 + 14 = 0 0 + x = 12.041594579 + 14 x = 12.041594579 + 14 Combine like terms: 12.041594579 + 14 = 26.041594579 x = 26.041594579 Simplifying x = 26.041594579Subproblem 2
x + -14 = -12.041594579 Simplifying x + -14 = -12.041594579 Reorder the terms: -14 + x = -12.041594579 Solving -14 + x = -12.041594579 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + x = -12.041594579 + 14 Combine like terms: -14 + 14 = 0 0 + x = -12.041594579 + 14 x = -12.041594579 + 14 Combine like terms: -12.041594579 + 14 = 1.958405421 x = 1.958405421 Simplifying x = 1.958405421Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.041594579, 1.958405421}Solution
x = {26.041594579, 1.958405421}
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