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Simplifying 0.2x2 + -0.4x + -0.51 = 0 Reorder the terms: -0.51 + -0.4x + 0.2x2 = 0 Solving -0.51 + -0.4x + 0.2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.2 the coefficient of the squared term: Divide each side by '0.2'. -2.55 + -2x + x2 = 0 Move the constant term to the right: Add '2.55' to each side of the equation. -2.55 + -2x + 2.55 + x2 = 0 + 2.55 Reorder the terms: -2.55 + 2.55 + -2x + x2 = 0 + 2.55 Combine like terms: -2.55 + 2.55 = 0.00 0.00 + -2x + x2 = 0 + 2.55 -2x + x2 = 0 + 2.55 Combine like terms: 0 + 2.55 = 2.55 -2x + x2 = 2.55 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 = 2.55 + 1 Reorder the terms: 1 + -2x + x2 = 2.55 + 1 Combine like terms: 2.55 + 1 = 3.55 1 + -2x + x2 = 3.55 Factor a perfect square on the left side: (x + -1)(x + -1) = 3.55 Calculate the square root of the right side: 1.884144368 Break this problem into two subproblems by setting (x + -1) equal to 1.884144368 and -1.884144368.Subproblem 1
x + -1 = 1.884144368 Simplifying x + -1 = 1.884144368 Reorder the terms: -1 + x = 1.884144368 Solving -1 + x = 1.884144368 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 = 1.884144368 + 1 Combine like terms: -1 + 1 = 0 0 + x = 1.884144368 + 1 x = 1.884144368 + 1 Combine like terms: 1.884144368 + 1 = 2.884144368 x = 2.884144368 Simplifying x = 2.884144368Subproblem 2
x + -1 = -1.884144368 Simplifying x + -1 = -1.884144368 Reorder the terms: -1 + x = -1.884144368 Solving -1 + x = -1.884144368 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 = -1.884144368 + 1 Combine like terms: -1 + 1 = 0 0 + x = -1.884144368 + 1 x = -1.884144368 + 1 Combine like terms: -1.884144368 + 1 = -0.884144368 x = -0.884144368 Simplifying x = -0.884144368Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.884144368, -0.884144368}
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