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Simplifying 5x2 + 6x + -60 = 0 Reorder the terms: -60 + 6x + 5x2 = 0 Solving -60 + 6x + 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 + 1.2x + x2 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + 1.2x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + 1.2x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 1.2x + x2 = 0 + 12 1.2x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 1.2x + x2 = 12 The x term is 1.2x. Take half its coefficient (0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. 1.2x + 0.36 + x2 = 12 + 0.36 Reorder the terms: 0.36 + 1.2x + x2 = 12 + 0.36 Combine like terms: 12 + 0.36 = 12.36 0.36 + 1.2x + x2 = 12.36 Factor a perfect square on the left side: (x + 0.6)(x + 0.6) = 12.36 Calculate the square root of the right side: 3.515679166 Break this problem into two subproblems by setting (x + 0.6) equal to 3.515679166 and -3.515679166.Subproblem 1
x + 0.6 = 3.515679166 Simplifying x + 0.6 = 3.515679166 Reorder the terms: 0.6 + x = 3.515679166 Solving 0.6 + x = 3.515679166 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + x = 3.515679166 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = 3.515679166 + -0.6 x = 3.515679166 + -0.6 Combine like terms: 3.515679166 + -0.6 = 2.915679166 x = 2.915679166 Simplifying x = 2.915679166Subproblem 2
x + 0.6 = -3.515679166 Simplifying x + 0.6 = -3.515679166 Reorder the terms: 0.6 + x = -3.515679166 Solving 0.6 + x = -3.515679166 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + x = -3.515679166 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = -3.515679166 + -0.6 x = -3.515679166 + -0.6 Combine like terms: -3.515679166 + -0.6 = -4.115679166 x = -4.115679166 Simplifying x = -4.115679166Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.915679166, -4.115679166}
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