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Simplifying 5x2 + 3x + -60 = 0 Reorder the terms: -60 + 3x + 5x2 = 0 Solving -60 + 3x + 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 + 0.6x + x2 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + 0.6x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + 0.6x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 0.6x + x2 = 0 + 12 0.6x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 0.6x + x2 = 12 The x term is 0.6x. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6x + 0.09 + x2 = 12 + 0.09 Reorder the terms: 0.09 + 0.6x + x2 = 12 + 0.09 Combine like terms: 12 + 0.09 = 12.09 0.09 + 0.6x + x2 = 12.09 Factor a perfect square on the left side: (x + 0.3)(x + 0.3) = 12.09 Calculate the square root of the right side: 3.47706773 Break this problem into two subproblems by setting (x + 0.3) equal to 3.47706773 and -3.47706773.Subproblem 1
x + 0.3 = 3.47706773 Simplifying x + 0.3 = 3.47706773 Reorder the terms: 0.3 + x = 3.47706773 Solving 0.3 + x = 3.47706773 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = 3.47706773 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = 3.47706773 + -0.3 x = 3.47706773 + -0.3 Combine like terms: 3.47706773 + -0.3 = 3.17706773 x = 3.17706773 Simplifying x = 3.17706773Subproblem 2
x + 0.3 = -3.47706773 Simplifying x + 0.3 = -3.47706773 Reorder the terms: 0.3 + x = -3.47706773 Solving 0.3 + x = -3.47706773 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = -3.47706773 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = -3.47706773 + -0.3 x = -3.47706773 + -0.3 Combine like terms: -3.47706773 + -0.3 = -3.77706773 x = -3.77706773 Simplifying x = -3.77706773Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.17706773, -3.77706773}
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