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Simplifying 5x2 + -2x + -155 = 0 Reorder the terms: -155 + -2x + 5x2 = 0 Solving -155 + -2x + 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'. -31 + -0.4x + x2 = 0 Move the constant term to the right: Add '31' to each side of the equation. -31 + -0.4x + 31 + x2 = 0 + 31 Reorder the terms: -31 + 31 + -0.4x + x2 = 0 + 31 Combine like terms: -31 + 31 = 0 0 + -0.4x + x2 = 0 + 31 -0.4x + x2 = 0 + 31 Combine like terms: 0 + 31 = 31 -0.4x + x2 = 31 The x term is -0.4x. Take half its coefficient (-0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. -0.4x + 0.04 + x2 = 31 + 0.04 Reorder the terms: 0.04 + -0.4x + x2 = 31 + 0.04 Combine like terms: 31 + 0.04 = 31.04 0.04 + -0.4x + x2 = 31.04 Factor a perfect square on the left side: (x + -0.2)(x + -0.2) = 31.04 Calculate the square root of the right side: 5.571355311 Break this problem into two subproblems by setting (x + -0.2) equal to 5.571355311 and -5.571355311.Subproblem 1
x + -0.2 = 5.571355311 Simplifying x + -0.2 = 5.571355311 Reorder the terms: -0.2 + x = 5.571355311 Solving -0.2 + x = 5.571355311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = 5.571355311 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = 5.571355311 + 0.2 x = 5.571355311 + 0.2 Combine like terms: 5.571355311 + 0.2 = 5.771355311 x = 5.771355311 Simplifying x = 5.771355311Subproblem 2
x + -0.2 = -5.571355311 Simplifying x + -0.2 = -5.571355311 Reorder the terms: -0.2 + x = -5.571355311 Solving -0.2 + x = -5.571355311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = -5.571355311 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = -5.571355311 + 0.2 x = -5.571355311 + 0.2 Combine like terms: -5.571355311 + 0.2 = -5.371355311 x = -5.371355311 Simplifying x = -5.371355311Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.771355311, -5.371355311}
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