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Simplifying -3x2 + 84x + -63 = 0 Reorder the terms: -63 + 84x + -3x2 = 0 Solving -63 + 84x + -3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-21 + 28x + -1x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-21 + 28x + -1x2)' equal to zero and attempt to solve: Simplifying -21 + 28x + -1x2 = 0 Solving -21 + 28x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 21 + -28x + x2 = 0 Move the constant term to the right: Add '-21' to each side of the equation. 21 + -28x + -21 + x2 = 0 + -21 Reorder the terms: 21 + -21 + -28x + x2 = 0 + -21 Combine like terms: 21 + -21 = 0 0 + -28x + x2 = 0 + -21 -28x + x2 = 0 + -21 Combine like terms: 0 + -21 = -21 -28x + x2 = -21 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 = -21 + 196 Reorder the terms: 196 + -28x + x2 = -21 + 196 Combine like terms: -21 + 196 = 175 196 + -28x + x2 = 175 Factor a perfect square on the left side: (x + -14)(x + -14) = 175 Calculate the square root of the right side: 13.228756555 Break this problem into two subproblems by setting (x + -14) equal to 13.228756555 and -13.228756555.Subproblem 1
x + -14 = 13.228756555 Simplifying x + -14 = 13.228756555 Reorder the terms: -14 + x = 13.228756555 Solving -14 + x = 13.228756555 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 = 13.228756555 + 14 Combine like terms: -14 + 14 = 0 0 + x = 13.228756555 + 14 x = 13.228756555 + 14 Combine like terms: 13.228756555 + 14 = 27.228756555 x = 27.228756555 Simplifying x = 27.228756555Subproblem 2
x + -14 = -13.228756555 Simplifying x + -14 = -13.228756555 Reorder the terms: -14 + x = -13.228756555 Solving -14 + x = -13.228756555 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 = -13.228756555 + 14 Combine like terms: -14 + 14 = 0 0 + x = -13.228756555 + 14 x = -13.228756555 + 14 Combine like terms: -13.228756555 + 14 = 0.771243445 x = 0.771243445 Simplifying x = 0.771243445Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.228756555, 0.771243445}Solution
x = {27.228756555, 0.771243445}
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