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Simplifying 5x2 + -10x + -3.14 = 0 Reorder the terms: -3.14 + -10x + 5x2 = 0 Solving -3.14 + -10x + 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'. -0.628 + -2x + x2 = 0 Move the constant term to the right: Add '0.628' to each side of the equation. -0.628 + -2x + 0.628 + x2 = 0 + 0.628 Reorder the terms: -0.628 + 0.628 + -2x + x2 = 0 + 0.628 Combine like terms: -0.628 + 0.628 = 0.000 0.000 + -2x + x2 = 0 + 0.628 -2x + x2 = 0 + 0.628 Combine like terms: 0 + 0.628 = 0.628 -2x + x2 = 0.628 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 0.628 + 1 Reorder the terms: 1 + -2x + x2 = 0.628 + 1 Combine like terms: 0.628 + 1 = 1.628 1 + -2x + x2 = 1.628 Factor a perfect square on the left side: (x + -1)(x + -1) = 1.628 Calculate the square root of the right side: 1.275931033 Break this problem into two subproblems by setting (x + -1) equal to 1.275931033 and -1.275931033.Subproblem 1
x + -1 = 1.275931033 Simplifying x + -1 = 1.275931033 Reorder the terms: -1 + x = 1.275931033 Solving -1 + x = 1.275931033 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 1.275931033 + 1 Combine like terms: -1 + 1 = 0 0 + x = 1.275931033 + 1 x = 1.275931033 + 1 Combine like terms: 1.275931033 + 1 = 2.275931033 x = 2.275931033 Simplifying x = 2.275931033Subproblem 2
x + -1 = -1.275931033 Simplifying x + -1 = -1.275931033 Reorder the terms: -1 + x = -1.275931033 Solving -1 + x = -1.275931033 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -1.275931033 + 1 Combine like terms: -1 + 1 = 0 0 + x = -1.275931033 + 1 x = -1.275931033 + 1 Combine like terms: -1.275931033 + 1 = -0.275931033 x = -0.275931033 Simplifying x = -0.275931033Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.275931033, -0.275931033}
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