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Simplifying 63x2 + -68x + -12 = 0 Reorder the terms: -12 + -68x + 63x2 = 0 Solving -12 + -68x + 63x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 63 the coefficient of the squared term: Divide each side by '63'. -0.1904761905 + -1.079365079x + x2 = 0 Move the constant term to the right: Add '0.1904761905' to each side of the equation. -0.1904761905 + -1.079365079x + 0.1904761905 + x2 = 0 + 0.1904761905 Reorder the terms: -0.1904761905 + 0.1904761905 + -1.079365079x + x2 = 0 + 0.1904761905 Combine like terms: -0.1904761905 + 0.1904761905 = 0.0000000000 0.0000000000 + -1.079365079x + x2 = 0 + 0.1904761905 -1.079365079x + x2 = 0 + 0.1904761905 Combine like terms: 0 + 0.1904761905 = 0.1904761905 -1.079365079x + x2 = 0.1904761905 The x term is -1.079365079x. Take half its coefficient (-0.5396825395). Square it (0.2912572434) and add it to both sides. Add '0.2912572434' to each side of the equation. -1.079365079x + 0.2912572434 + x2 = 0.1904761905 + 0.2912572434 Reorder the terms: 0.2912572434 + -1.079365079x + x2 = 0.1904761905 + 0.2912572434 Combine like terms: 0.1904761905 + 0.2912572434 = 0.4817334339 0.2912572434 + -1.079365079x + x2 = 0.4817334339 Factor a perfect square on the left side: (x + -0.5396825395)(x + -0.5396825395) = 0.4817334339 Calculate the square root of the right side: 0.694070194 Break this problem into two subproblems by setting (x + -0.5396825395) equal to 0.694070194 and -0.694070194.Subproblem 1
x + -0.5396825395 = 0.694070194 Simplifying x + -0.5396825395 = 0.694070194 Reorder the terms: -0.5396825395 + x = 0.694070194 Solving -0.5396825395 + x = 0.694070194 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5396825395' to each side of the equation. -0.5396825395 + 0.5396825395 + x = 0.694070194 + 0.5396825395 Combine like terms: -0.5396825395 + 0.5396825395 = 0.0000000000 0.0000000000 + x = 0.694070194 + 0.5396825395 x = 0.694070194 + 0.5396825395 Combine like terms: 0.694070194 + 0.5396825395 = 1.2337527335 x = 1.2337527335 Simplifying x = 1.2337527335Subproblem 2
x + -0.5396825395 = -0.694070194 Simplifying x + -0.5396825395 = -0.694070194 Reorder the terms: -0.5396825395 + x = -0.694070194 Solving -0.5396825395 + x = -0.694070194 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5396825395' to each side of the equation. -0.5396825395 + 0.5396825395 + x = -0.694070194 + 0.5396825395 Combine like terms: -0.5396825395 + 0.5396825395 = 0.0000000000 0.0000000000 + x = -0.694070194 + 0.5396825395 x = -0.694070194 + 0.5396825395 Combine like terms: -0.694070194 + 0.5396825395 = -0.1543876545 x = -0.1543876545 Simplifying x = -0.1543876545Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2337527335, -0.1543876545}
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