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Simplifying 25x2 + -30x + -36 = 0 Reorder the terms: -36 + -30x + 25x2 = 0 Solving -36 + -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'. -1.44 + -1.2x + x2 = 0 Move the constant term to the right: Add '1.44' to each side of the equation. -1.44 + -1.2x + 1.44 + x2 = 0 + 1.44 Reorder the terms: -1.44 + 1.44 + -1.2x + x2 = 0 + 1.44 Combine like terms: -1.44 + 1.44 = 0.00 0.00 + -1.2x + x2 = 0 + 1.44 -1.2x + x2 = 0 + 1.44 Combine like terms: 0 + 1.44 = 1.44 -1.2x + x2 = 1.44 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 = 1.44 + 0.36 Reorder the terms: 0.36 + -1.2x + x2 = 1.44 + 0.36 Combine like terms: 1.44 + 0.36 = 1.8 0.36 + -1.2x + x2 = 1.8 Factor a perfect square on the left side: (x + -0.6)(x + -0.6) = 1.8 Calculate the square root of the right side: 1.341640787 Break this problem into two subproblems by setting (x + -0.6) equal to 1.341640787 and -1.341640787.Subproblem 1
x + -0.6 = 1.341640787 Simplifying x + -0.6 = 1.341640787 Reorder the terms: -0.6 + x = 1.341640787 Solving -0.6 + x = 1.341640787 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 = 1.341640787 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = 1.341640787 + 0.6 x = 1.341640787 + 0.6 Combine like terms: 1.341640787 + 0.6 = 1.941640787 x = 1.941640787 Simplifying x = 1.941640787Subproblem 2
x + -0.6 = -1.341640787 Simplifying x + -0.6 = -1.341640787 Reorder the terms: -0.6 + x = -1.341640787 Solving -0.6 + x = -1.341640787 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 = -1.341640787 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = -1.341640787 + 0.6 x = -1.341640787 + 0.6 Combine like terms: -1.341640787 + 0.6 = -0.741640787 x = -0.741640787 Simplifying x = -0.741640787Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.941640787, -0.741640787}
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