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Simplifying 5x2 + 3x + -15 = 80 Reorder the terms: -15 + 3x + 5x2 = 80 Solving -15 + 3x + 5x2 = 80 Solving for variable 'x'. Reorder the terms: -15 + -80 + 3x + 5x2 = 80 + -80 Combine like terms: -15 + -80 = -95 -95 + 3x + 5x2 = 80 + -80 Combine like terms: 80 + -80 = 0 -95 + 3x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -19 + 0.6x + x2 = 0 Move the constant term to the right: Add '19' to each side of the equation. -19 + 0.6x + 19 + x2 = 0 + 19 Reorder the terms: -19 + 19 + 0.6x + x2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + 0.6x + x2 = 0 + 19 0.6x + x2 = 0 + 19 Combine like terms: 0 + 19 = 19 0.6x + x2 = 19 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 = 19 + 0.09 Reorder the terms: 0.09 + 0.6x + x2 = 19 + 0.09 Combine like terms: 19 + 0.09 = 19.09 0.09 + 0.6x + x2 = 19.09 Factor a perfect square on the left side: (x + 0.3)(x + 0.3) = 19.09 Calculate the square root of the right side: 4.369210455 Break this problem into two subproblems by setting (x + 0.3) equal to 4.369210455 and -4.369210455.Subproblem 1
x + 0.3 = 4.369210455 Simplifying x + 0.3 = 4.369210455 Reorder the terms: 0.3 + x = 4.369210455 Solving 0.3 + x = 4.369210455 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 = 4.369210455 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = 4.369210455 + -0.3 x = 4.369210455 + -0.3 Combine like terms: 4.369210455 + -0.3 = 4.069210455 x = 4.069210455 Simplifying x = 4.069210455Subproblem 2
x + 0.3 = -4.369210455 Simplifying x + 0.3 = -4.369210455 Reorder the terms: 0.3 + x = -4.369210455 Solving 0.3 + x = -4.369210455 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 = -4.369210455 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = -4.369210455 + -0.3 x = -4.369210455 + -0.3 Combine like terms: -4.369210455 + -0.3 = -4.669210455 x = -4.669210455 Simplifying x = -4.669210455Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.069210455, -4.669210455}
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