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Simplifying -1x2 + 2.4x + 24.333 = 0 Reorder the terms: 24.333 + 2.4x + -1x2 = 0 Solving 24.333 + 2.4x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -24.333 + -2.4x + x2 = 0 Move the constant term to the right: Add '24.333' to each side of the equation. -24.333 + -2.4x + 24.333 + x2 = 0 + 24.333 Reorder the terms: -24.333 + 24.333 + -2.4x + x2 = 0 + 24.333 Combine like terms: -24.333 + 24.333 = 0.000 0.000 + -2.4x + x2 = 0 + 24.333 -2.4x + x2 = 0 + 24.333 Combine like terms: 0 + 24.333 = 24.333 -2.4x + x2 = 24.333 The x term is -2.4x. Take half its coefficient (-1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. -2.4x + 1.44 + x2 = 24.333 + 1.44 Reorder the terms: 1.44 + -2.4x + x2 = 24.333 + 1.44 Combine like terms: 24.333 + 1.44 = 25.773 1.44 + -2.4x + x2 = 25.773 Factor a perfect square on the left side: (x + -1.2)(x + -1.2) = 25.773 Calculate the square root of the right side: 5.076711534 Break this problem into two subproblems by setting (x + -1.2) equal to 5.076711534 and -5.076711534.Subproblem 1
x + -1.2 = 5.076711534 Simplifying x + -1.2 = 5.076711534 Reorder the terms: -1.2 + x = 5.076711534 Solving -1.2 + x = 5.076711534 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + x = 5.076711534 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = 5.076711534 + 1.2 x = 5.076711534 + 1.2 Combine like terms: 5.076711534 + 1.2 = 6.276711534 x = 6.276711534 Simplifying x = 6.276711534Subproblem 2
x + -1.2 = -5.076711534 Simplifying x + -1.2 = -5.076711534 Reorder the terms: -1.2 + x = -5.076711534 Solving -1.2 + x = -5.076711534 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + x = -5.076711534 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = -5.076711534 + 1.2 x = -5.076711534 + 1.2 Combine like terms: -5.076711534 + 1.2 = -3.876711534 x = -3.876711534 Simplifying x = -3.876711534Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.276711534, -3.876711534}
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