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Simplifying 63x2 + 24x + -29 = 0 Reorder the terms: -29 + 24x + 63x2 = 0 Solving -29 + 24x + 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'. -0.4603174603 + 0.380952381x + x2 = 0 Move the constant term to the right: Add '0.4603174603' to each side of the equation. -0.4603174603 + 0.380952381x + 0.4603174603 + x2 = 0 + 0.4603174603 Reorder the terms: -0.4603174603 + 0.4603174603 + 0.380952381x + x2 = 0 + 0.4603174603 Combine like terms: -0.4603174603 + 0.4603174603 = 0.0000000000 0.0000000000 + 0.380952381x + x2 = 0 + 0.4603174603 0.380952381x + x2 = 0 + 0.4603174603 Combine like terms: 0 + 0.4603174603 = 0.4603174603 0.380952381x + x2 = 0.4603174603 The x term is 0.380952381x. Take half its coefficient (0.1904761905). Square it (0.03628117915) and add it to both sides. Add '0.03628117915' to each side of the equation. 0.380952381x + 0.03628117915 + x2 = 0.4603174603 + 0.03628117915 Reorder the terms: 0.03628117915 + 0.380952381x + x2 = 0.4603174603 + 0.03628117915 Combine like terms: 0.4603174603 + 0.03628117915 = 0.49659863945 0.03628117915 + 0.380952381x + x2 = 0.49659863945 Factor a perfect square on the left side: (x + 0.1904761905)(x + 0.1904761905) = 0.49659863945 Calculate the square root of the right side: 0.704697552 Break this problem into two subproblems by setting (x + 0.1904761905) equal to 0.704697552 and -0.704697552.Subproblem 1
x + 0.1904761905 = 0.704697552 Simplifying x + 0.1904761905 = 0.704697552 Reorder the terms: 0.1904761905 + x = 0.704697552 Solving 0.1904761905 + x = 0.704697552 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1904761905' to each side of the equation. 0.1904761905 + -0.1904761905 + x = 0.704697552 + -0.1904761905 Combine like terms: 0.1904761905 + -0.1904761905 = 0.0000000000 0.0000000000 + x = 0.704697552 + -0.1904761905 x = 0.704697552 + -0.1904761905 Combine like terms: 0.704697552 + -0.1904761905 = 0.5142213615 x = 0.5142213615 Simplifying x = 0.5142213615Subproblem 2
x + 0.1904761905 = -0.704697552 Simplifying x + 0.1904761905 = -0.704697552 Reorder the terms: 0.1904761905 + x = -0.704697552 Solving 0.1904761905 + x = -0.704697552 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1904761905' to each side of the equation. 0.1904761905 + -0.1904761905 + x = -0.704697552 + -0.1904761905 Combine like terms: 0.1904761905 + -0.1904761905 = 0.0000000000 0.0000000000 + x = -0.704697552 + -0.1904761905 x = -0.704697552 + -0.1904761905 Combine like terms: -0.704697552 + -0.1904761905 = -0.8951737425 x = -0.8951737425 Simplifying x = -0.8951737425Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5142213615, -0.8951737425}
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