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Simplifying x2 + x + -1220 * 4 = 0 Multiply -1220 * 4 x2 + x + -4880 = 0 Reorder the terms: -4880 + x + x2 = 0 Solving -4880 + x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '4880' to each side of the equation. -4880 + x + 4880 + x2 = 0 + 4880 Reorder the terms: -4880 + 4880 + x + x2 = 0 + 4880 Combine like terms: -4880 + 4880 = 0 0 + x + x2 = 0 + 4880 x + x2 = 0 + 4880 Combine like terms: 0 + 4880 = 4880 x + x2 = 4880 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 = 4880 + 0.25 Reorder the terms: 0.25 + x + x2 = 4880 + 0.25 Combine like terms: 4880 + 0.25 = 4880.25 0.25 + x + x2 = 4880.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 4880.25 Calculate the square root of the right side: 69.858786133 Break this problem into two subproblems by setting (x + 0.5) equal to 69.858786133 and -69.858786133.Subproblem 1
x + 0.5 = 69.858786133 Simplifying x + 0.5 = 69.858786133 Reorder the terms: 0.5 + x = 69.858786133 Solving 0.5 + x = 69.858786133 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 = 69.858786133 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 69.858786133 + -0.5 x = 69.858786133 + -0.5 Combine like terms: 69.858786133 + -0.5 = 69.358786133 x = 69.358786133 Simplifying x = 69.358786133Subproblem 2
x + 0.5 = -69.858786133 Simplifying x + 0.5 = -69.858786133 Reorder the terms: 0.5 + x = -69.858786133 Solving 0.5 + x = -69.858786133 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 = -69.858786133 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -69.858786133 + -0.5 x = -69.858786133 + -0.5 Combine like terms: -69.858786133 + -0.5 = -70.358786133 x = -70.358786133 Simplifying x = -70.358786133Solution
The solution to the problem is based on the solutions from the subproblems. x = {69.358786133, -70.358786133}
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