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Simplifying -5x2 + -3x + 1 = 0 Reorder the terms: 1 + -3x + -5x2 = 0 Solving 1 + -3x + -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'. -0.2 + 0.6x + x2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + 0.6x + 0.2 + x2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + 0.6x + x2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + 0.6x + x2 = 0 + 0.2 0.6x + x2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 0.6x + x2 = 0.2 The x term is 0.6x. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6x + 0.09 + x2 = 0.2 + 0.09 Reorder the terms: 0.09 + 0.6x + x2 = 0.2 + 0.09 Combine like terms: 0.2 + 0.09 = 0.29 0.09 + 0.6x + x2 = 0.29 Factor a perfect square on the left side: (x + 0.3)(x + 0.3) = 0.29 Calculate the square root of the right side: 0.538516481 Break this problem into two subproblems by setting (x + 0.3) equal to 0.538516481 and -0.538516481.Subproblem 1
x + 0.3 = 0.538516481 Simplifying x + 0.3 = 0.538516481 Reorder the terms: 0.3 + x = 0.538516481 Solving 0.3 + x = 0.538516481 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = 0.538516481 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = 0.538516481 + -0.3 x = 0.538516481 + -0.3 Combine like terms: 0.538516481 + -0.3 = 0.238516481 x = 0.238516481 Simplifying x = 0.238516481Subproblem 2
x + 0.3 = -0.538516481 Simplifying x + 0.3 = -0.538516481 Reorder the terms: 0.3 + x = -0.538516481 Solving 0.3 + x = -0.538516481 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = -0.538516481 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = -0.538516481 + -0.3 x = -0.538516481 + -0.3 Combine like terms: -0.538516481 + -0.3 = -0.838516481 x = -0.838516481 Simplifying x = -0.838516481Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.238516481, -0.838516481}
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