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Simplifying 5x2 + -62x + -7 = 0 Reorder the terms: -7 + -62x + 5x2 = 0 Solving -7 + -62x + 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'. -1.4 + -12.4x + x2 = 0 Move the constant term to the right: Add '1.4' to each side of the equation. -1.4 + -12.4x + 1.4 + x2 = 0 + 1.4 Reorder the terms: -1.4 + 1.4 + -12.4x + x2 = 0 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + -12.4x + x2 = 0 + 1.4 -12.4x + x2 = 0 + 1.4 Combine like terms: 0 + 1.4 = 1.4 -12.4x + x2 = 1.4 The x term is -12.4x. Take half its coefficient (-6.2). Square it (38.44) and add it to both sides. Add '38.44' to each side of the equation. -12.4x + 38.44 + x2 = 1.4 + 38.44 Reorder the terms: 38.44 + -12.4x + x2 = 1.4 + 38.44 Combine like terms: 1.4 + 38.44 = 39.84 38.44 + -12.4x + x2 = 39.84 Factor a perfect square on the left side: (x + -6.2)(x + -6.2) = 39.84 Calculate the square root of the right side: 6.311893535 Break this problem into two subproblems by setting (x + -6.2) equal to 6.311893535 and -6.311893535.Subproblem 1
x + -6.2 = 6.311893535 Simplifying x + -6.2 = 6.311893535 Reorder the terms: -6.2 + x = 6.311893535 Solving -6.2 + x = 6.311893535 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.2' to each side of the equation. -6.2 + 6.2 + x = 6.311893535 + 6.2 Combine like terms: -6.2 + 6.2 = 0.0 0.0 + x = 6.311893535 + 6.2 x = 6.311893535 + 6.2 Combine like terms: 6.311893535 + 6.2 = 12.511893535 x = 12.511893535 Simplifying x = 12.511893535Subproblem 2
x + -6.2 = -6.311893535 Simplifying x + -6.2 = -6.311893535 Reorder the terms: -6.2 + x = -6.311893535 Solving -6.2 + x = -6.311893535 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.2' to each side of the equation. -6.2 + 6.2 + x = -6.311893535 + 6.2 Combine like terms: -6.2 + 6.2 = 0.0 0.0 + x = -6.311893535 + 6.2 x = -6.311893535 + 6.2 Combine like terms: -6.311893535 + 6.2 = -0.111893535 x = -0.111893535 Simplifying x = -0.111893535Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.511893535, -0.111893535}
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