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Simplifying 5x2 + 6x + -40 = 0 Reorder the terms: -40 + 6x + 5x2 = 0 Solving -40 + 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'. -8 + 1.2x + x2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + 1.2x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + 1.2x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 1.2x + x2 = 0 + 8 1.2x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 1.2x + x2 = 8 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 = 8 + 0.36 Reorder the terms: 0.36 + 1.2x + x2 = 8 + 0.36 Combine like terms: 8 + 0.36 = 8.36 0.36 + 1.2x + x2 = 8.36 Factor a perfect square on the left side: (x + 0.6)(x + 0.6) = 8.36 Calculate the square root of the right side: 2.891366459 Break this problem into two subproblems by setting (x + 0.6) equal to 2.891366459 and -2.891366459.Subproblem 1
x + 0.6 = 2.891366459 Simplifying x + 0.6 = 2.891366459 Reorder the terms: 0.6 + x = 2.891366459 Solving 0.6 + x = 2.891366459 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 = 2.891366459 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = 2.891366459 + -0.6 x = 2.891366459 + -0.6 Combine like terms: 2.891366459 + -0.6 = 2.291366459 x = 2.291366459 Simplifying x = 2.291366459Subproblem 2
x + 0.6 = -2.891366459 Simplifying x + 0.6 = -2.891366459 Reorder the terms: 0.6 + x = -2.891366459 Solving 0.6 + x = -2.891366459 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 = -2.891366459 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = -2.891366459 + -0.6 x = -2.891366459 + -0.6 Combine like terms: -2.891366459 + -0.6 = -3.491366459 x = -3.491366459 Simplifying x = -3.491366459Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.291366459, -3.491366459}
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