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Simplifying 5x2 + 3x + -80 = 0 Reorder the terms: -80 + 3x + 5x2 = 0 Solving -80 + 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'. -16 + 0.6x + x2 = 0 Move the constant term to the right: Add '16' to each side of the equation. -16 + 0.6x + 16 + x2 = 0 + 16 Reorder the terms: -16 + 16 + 0.6x + x2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 0.6x + x2 = 0 + 16 0.6x + x2 = 0 + 16 Combine like terms: 0 + 16 = 16 0.6x + x2 = 16 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 = 16 + 0.09 Reorder the terms: 0.09 + 0.6x + x2 = 16 + 0.09 Combine like terms: 16 + 0.09 = 16.09 0.09 + 0.6x + x2 = 16.09 Factor a perfect square on the left side: (x + 0.3)(x + 0.3) = 16.09 Calculate the square root of the right side: 4.011234224 Break this problem into two subproblems by setting (x + 0.3) equal to 4.011234224 and -4.011234224.Subproblem 1
x + 0.3 = 4.011234224 Simplifying x + 0.3 = 4.011234224 Reorder the terms: 0.3 + x = 4.011234224 Solving 0.3 + x = 4.011234224 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 = 4.011234224 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = 4.011234224 + -0.3 x = 4.011234224 + -0.3 Combine like terms: 4.011234224 + -0.3 = 3.711234224 x = 3.711234224 Simplifying x = 3.711234224Subproblem 2
x + 0.3 = -4.011234224 Simplifying x + 0.3 = -4.011234224 Reorder the terms: 0.3 + x = -4.011234224 Solving 0.3 + x = -4.011234224 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 = -4.011234224 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = -4.011234224 + -0.3 x = -4.011234224 + -0.3 Combine like terms: -4.011234224 + -0.3 = -4.311234224 x = -4.311234224 Simplifying x = -4.311234224Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.711234224, -4.311234224}
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