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Simplifying 5x2 + 5x + -63 = 0 Reorder the terms: -63 + 5x + 5x2 = 0 Solving -63 + 5x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -12.6 + x + x2 = 0 Move the constant term to the right: Add '12.6' to each side of the equation. -12.6 + x + 12.6 + x2 = 0 + 12.6 Reorder the terms: -12.6 + 12.6 + x + x2 = 0 + 12.6 Combine like terms: -12.6 + 12.6 = 0.0 0.0 + x + x2 = 0 + 12.6 x + x2 = 0 + 12.6 Combine like terms: 0 + 12.6 = 12.6 x + x2 = 12.6 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 12.6 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 12.6 + 0.25 Combine like terms: 12.6 + 0.25 = 12.85 1.25 + x2 = 12.85 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 12.85 Calculate the square root of the right side: 3.584689666 Break this problem into two subproblems by setting (x + 0.5) equal to 3.584689666 and -3.584689666.Subproblem 1
x + 0.5 = 3.584689666 Simplifying x + 0.5 = 3.584689666 Reorder the terms: 0.5 + x = 3.584689666 Solving 0.5 + x = 3.584689666 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 3.584689666 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 3.584689666 + -0.5 x = 3.584689666 + -0.5 Combine like terms: 3.584689666 + -0.5 = 3.084689666 x = 3.084689666 Simplifying x = 3.084689666Subproblem 2
x + 0.5 = -3.584689666 Simplifying x + 0.5 = -3.584689666 Reorder the terms: 0.5 + x = -3.584689666 Solving 0.5 + x = -3.584689666 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -3.584689666 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -3.584689666 + -0.5 x = -3.584689666 + -0.5 Combine like terms: -3.584689666 + -0.5 = -4.084689666 x = -4.084689666 Simplifying x = -4.084689666Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.084689666, -4.084689666}
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