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Simplifying 25x2 + -30x + -2 = 0 Reorder the terms: -2 + -30x + 25x2 = 0 Solving -2 + -30x + 25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -0.08 + -1.2x + x2 = 0 Move the constant term to the right: Add '0.08' to each side of the equation. -0.08 + -1.2x + 0.08 + x2 = 0 + 0.08 Reorder the terms: -0.08 + 0.08 + -1.2x + x2 = 0 + 0.08 Combine like terms: -0.08 + 0.08 = 0.00 0.00 + -1.2x + x2 = 0 + 0.08 -1.2x + x2 = 0 + 0.08 Combine like terms: 0 + 0.08 = 0.08 -1.2x + x2 = 0.08 The x term is -1.2x. Take half its coefficient (-0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. -1.2x + 0.36 + x2 = 0.08 + 0.36 Reorder the terms: 0.36 + -1.2x + x2 = 0.08 + 0.36 Combine like terms: 0.08 + 0.36 = 0.44 0.36 + -1.2x + x2 = 0.44 Factor a perfect square on the left side: (x + -0.6)(x + -0.6) = 0.44 Calculate the square root of the right side: 0.663324958 Break this problem into two subproblems by setting (x + -0.6) equal to 0.663324958 and -0.663324958.Subproblem 1
x + -0.6 = 0.663324958 Simplifying x + -0.6 = 0.663324958 Reorder the terms: -0.6 + x = 0.663324958 Solving -0.6 + x = 0.663324958 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = 0.663324958 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = 0.663324958 + 0.6 x = 0.663324958 + 0.6 Combine like terms: 0.663324958 + 0.6 = 1.263324958 x = 1.263324958 Simplifying x = 1.263324958Subproblem 2
x + -0.6 = -0.663324958 Simplifying x + -0.6 = -0.663324958 Reorder the terms: -0.6 + x = -0.663324958 Solving -0.6 + x = -0.663324958 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = -0.663324958 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = -0.663324958 + 0.6 x = -0.663324958 + 0.6 Combine like terms: -0.663324958 + 0.6 = -0.063324958 x = -0.063324958 Simplifying x = -0.063324958Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.263324958, -0.063324958}
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