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Simplifying 5x2 + -6x + -76 = 0 Reorder the terms: -76 + -6x + 5x2 = 0 Solving -76 + -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'. -15.2 + -1.2x + x2 = 0 Move the constant term to the right: Add '15.2' to each side of the equation. -15.2 + -1.2x + 15.2 + x2 = 0 + 15.2 Reorder the terms: -15.2 + 15.2 + -1.2x + x2 = 0 + 15.2 Combine like terms: -15.2 + 15.2 = 0.0 0.0 + -1.2x + x2 = 0 + 15.2 -1.2x + x2 = 0 + 15.2 Combine like terms: 0 + 15.2 = 15.2 -1.2x + x2 = 15.2 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 = 15.2 + 0.36 Reorder the terms: 0.36 + -1.2x + x2 = 15.2 + 0.36 Combine like terms: 15.2 + 0.36 = 15.56 0.36 + -1.2x + x2 = 15.56 Factor a perfect square on the left side: (x + -0.6)(x + -0.6) = 15.56 Calculate the square root of the right side: 3.944616585 Break this problem into two subproblems by setting (x + -0.6) equal to 3.944616585 and -3.944616585.Subproblem 1
x + -0.6 = 3.944616585 Simplifying x + -0.6 = 3.944616585 Reorder the terms: -0.6 + x = 3.944616585 Solving -0.6 + x = 3.944616585 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 = 3.944616585 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = 3.944616585 + 0.6 x = 3.944616585 + 0.6 Combine like terms: 3.944616585 + 0.6 = 4.544616585 x = 4.544616585 Simplifying x = 4.544616585Subproblem 2
x + -0.6 = -3.944616585 Simplifying x + -0.6 = -3.944616585 Reorder the terms: -0.6 + x = -3.944616585 Solving -0.6 + x = -3.944616585 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 = -3.944616585 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = -3.944616585 + 0.6 x = -3.944616585 + 0.6 Combine like terms: -3.944616585 + 0.6 = -3.344616585 x = -3.344616585 Simplifying x = -3.344616585Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.544616585, -3.344616585}
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