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Simplifying x2 + x + -510 = 0 Reorder the terms: -510 + x + x2 = 0 Solving -510 + x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '510' to each side of the equation. -510 + x + 510 + x2 = 0 + 510 Reorder the terms: -510 + 510 + x + x2 = 0 + 510 Combine like terms: -510 + 510 = 0 0 + x + x2 = 0 + 510 x + x2 = 0 + 510 Combine like terms: 0 + 510 = 510 x + x2 = 510 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x + 0.25 + x2 = 510 + 0.25 Reorder the terms: 0.25 + x + x2 = 510 + 0.25 Combine like terms: 510 + 0.25 = 510.25 0.25 + x + x2 = 510.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 510.25 Calculate the square root of the right side: 22.588713996 Break this problem into two subproblems by setting (x + 0.5) equal to 22.588713996 and -22.588713996.Subproblem 1
x + 0.5 = 22.588713996 Simplifying x + 0.5 = 22.588713996 Reorder the terms: 0.5 + x = 22.588713996 Solving 0.5 + x = 22.588713996 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 22.588713996 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 22.588713996 + -0.5 x = 22.588713996 + -0.5 Combine like terms: 22.588713996 + -0.5 = 22.088713996 x = 22.088713996 Simplifying x = 22.088713996Subproblem 2
x + 0.5 = -22.588713996 Simplifying x + 0.5 = -22.588713996 Reorder the terms: 0.5 + x = -22.588713996 Solving 0.5 + x = -22.588713996 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -22.588713996 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -22.588713996 + -0.5 x = -22.588713996 + -0.5 Combine like terms: -22.588713996 + -0.5 = -23.088713996 x = -23.088713996 Simplifying x = -23.088713996Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.088713996, -23.088713996}
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