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Simplifying 5x2 + 7x + -60 = 0 Reorder the terms: -60 + 7x + 5x2 = 0 Solving -60 + 7x + 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 + 1.4x + x2 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + 1.4x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + 1.4x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 1.4x + x2 = 0 + 12 1.4x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 1.4x + x2 = 12 The x term is 1.4x. Take half its coefficient (0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. 1.4x + 0.49 + x2 = 12 + 0.49 Reorder the terms: 0.49 + 1.4x + x2 = 12 + 0.49 Combine like terms: 12 + 0.49 = 12.49 0.49 + 1.4x + x2 = 12.49 Factor a perfect square on the left side: (x + 0.7)(x + 0.7) = 12.49 Calculate the square root of the right side: 3.534119409 Break this problem into two subproblems by setting (x + 0.7) equal to 3.534119409 and -3.534119409.Subproblem 1
x + 0.7 = 3.534119409 Simplifying x + 0.7 = 3.534119409 Reorder the terms: 0.7 + x = 3.534119409 Solving 0.7 + x = 3.534119409 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7' to each side of the equation. 0.7 + -0.7 + x = 3.534119409 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + x = 3.534119409 + -0.7 x = 3.534119409 + -0.7 Combine like terms: 3.534119409 + -0.7 = 2.834119409 x = 2.834119409 Simplifying x = 2.834119409Subproblem 2
x + 0.7 = -3.534119409 Simplifying x + 0.7 = -3.534119409 Reorder the terms: 0.7 + x = -3.534119409 Solving 0.7 + x = -3.534119409 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7' to each side of the equation. 0.7 + -0.7 + x = -3.534119409 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + x = -3.534119409 + -0.7 x = -3.534119409 + -0.7 Combine like terms: -3.534119409 + -0.7 = -4.234119409 x = -4.234119409 Simplifying x = -4.234119409Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.834119409, -4.234119409}
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