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Simplifying -24x2 + 72x = 5 Reorder the terms: 72x + -24x2 = 5 Solving 72x + -24x2 = 5 Solving for variable 'x'. Reorder the terms: -5 + 72x + -24x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + 72x + -24x2 = 0 Begin completing the square. Divide all terms by -24 the coefficient of the squared term: Divide each side by '-24'. 0.2083333333 + -3x + x2 = 0 Move the constant term to the right: Add '-0.2083333333' to each side of the equation. 0.2083333333 + -3x + -0.2083333333 + x2 = 0 + -0.2083333333 Reorder the terms: 0.2083333333 + -0.2083333333 + -3x + x2 = 0 + -0.2083333333 Combine like terms: 0.2083333333 + -0.2083333333 = 0.0000000000 0.0000000000 + -3x + x2 = 0 + -0.2083333333 -3x + x2 = 0 + -0.2083333333 Combine like terms: 0 + -0.2083333333 = -0.2083333333 -3x + x2 = -0.2083333333 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = -0.2083333333 + 2.25 Reorder the terms: 2.25 + -3x + x2 = -0.2083333333 + 2.25 Combine like terms: -0.2083333333 + 2.25 = 2.0416666667 2.25 + -3x + x2 = 2.0416666667 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 2.0416666667 Calculate the square root of the right side: 1.428869017 Break this problem into two subproblems by setting (x + -1.5) equal to 1.428869017 and -1.428869017.Subproblem 1
x + -1.5 = 1.428869017 Simplifying x + -1.5 = 1.428869017 Reorder the terms: -1.5 + x = 1.428869017 Solving -1.5 + x = 1.428869017 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 1.428869017 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 1.428869017 + 1.5 x = 1.428869017 + 1.5 Combine like terms: 1.428869017 + 1.5 = 2.928869017 x = 2.928869017 Simplifying x = 2.928869017Subproblem 2
x + -1.5 = -1.428869017 Simplifying x + -1.5 = -1.428869017 Reorder the terms: -1.5 + x = -1.428869017 Solving -1.5 + x = -1.428869017 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -1.428869017 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -1.428869017 + 1.5 x = -1.428869017 + 1.5 Combine like terms: -1.428869017 + 1.5 = 0.071130983 x = 0.071130983 Simplifying x = 0.071130983Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.928869017, 0.071130983}
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