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Simplifying 5x2 + 8x + -670 = 0 Reorder the terms: -670 + 8x + 5x2 = 0 Solving -670 + 8x + 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'. -134 + 1.6x + x2 = 0 Move the constant term to the right: Add '134' to each side of the equation. -134 + 1.6x + 134 + x2 = 0 + 134 Reorder the terms: -134 + 134 + 1.6x + x2 = 0 + 134 Combine like terms: -134 + 134 = 0 0 + 1.6x + x2 = 0 + 134 1.6x + x2 = 0 + 134 Combine like terms: 0 + 134 = 134 1.6x + x2 = 134 The x term is 1.6x. Take half its coefficient (0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. 1.6x + 0.64 + x2 = 134 + 0.64 Reorder the terms: 0.64 + 1.6x + x2 = 134 + 0.64 Combine like terms: 134 + 0.64 = 134.64 0.64 + 1.6x + x2 = 134.64 Factor a perfect square on the left side: (x + 0.8)(x + 0.8) = 134.64 Calculate the square root of the right side: 11.603447763 Break this problem into two subproblems by setting (x + 0.8) equal to 11.603447763 and -11.603447763.Subproblem 1
x + 0.8 = 11.603447763 Simplifying x + 0.8 = 11.603447763 Reorder the terms: 0.8 + x = 11.603447763 Solving 0.8 + x = 11.603447763 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + x = 11.603447763 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = 11.603447763 + -0.8 x = 11.603447763 + -0.8 Combine like terms: 11.603447763 + -0.8 = 10.803447763 x = 10.803447763 Simplifying x = 10.803447763Subproblem 2
x + 0.8 = -11.603447763 Simplifying x + 0.8 = -11.603447763 Reorder the terms: 0.8 + x = -11.603447763 Solving 0.8 + x = -11.603447763 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + x = -11.603447763 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = -11.603447763 + -0.8 x = -11.603447763 + -0.8 Combine like terms: -11.603447763 + -0.8 = -12.403447763 x = -12.403447763 Simplifying x = -12.403447763Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.803447763, -12.403447763}
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