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Simplifying 0.3x2 + -33x + 15.000 = 22.800 Reorder the terms: 15.000 + -33x + 0.3x2 = 22.800 Solving 15.000 + -33x + 0.3x2 = 22.800 Solving for variable 'x'. Reorder the terms: 15.000 + -22.800 + -33x + 0.3x2 = 22.800 + -22.800 Combine like terms: 15.000 + -22.800 = -7.8 -7.8 + -33x + 0.3x2 = 22.800 + -22.800 Combine like terms: 22.800 + -22.800 = 0.000 -7.8 + -33x + 0.3x2 = 0.000 Begin completing the square. Divide all terms by 0.3 the coefficient of the squared term: Divide each side by '0.3'. -26 + -110x + x2 = 0.00 Move the constant term to the right: Add '26' to each side of the equation. -26 + -110x + 26 + x2 = 0.00 + 26 Reorder the terms: -26 + 26 + -110x + x2 = 0.00 + 26 Combine like terms: -26 + 26 = 0 0 + -110x + x2 = 0.00 + 26 -110x + x2 = 0.00 + 26 Combine like terms: 0.00 + 26 = 26 -110x + x2 = 26 The x term is -110x. Take half its coefficient (-55). Square it (3025) and add it to both sides. Add '3025' to each side of the equation. -110x + 3025 + x2 = 26 + 3025 Reorder the terms: 3025 + -110x + x2 = 26 + 3025 Combine like terms: 26 + 3025 = 3051 3025 + -110x + x2 = 3051 Factor a perfect square on the left side: (x + -55)(x + -55) = 3051 Calculate the square root of the right side: 55.235857919 Break this problem into two subproblems by setting (x + -55) equal to 55.235857919 and -55.235857919.Subproblem 1
x + -55 = 55.235857919 Simplifying x + -55 = 55.235857919 Reorder the terms: -55 + x = 55.235857919 Solving -55 + x = 55.235857919 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '55' to each side of the equation. -55 + 55 + x = 55.235857919 + 55 Combine like terms: -55 + 55 = 0 0 + x = 55.235857919 + 55 x = 55.235857919 + 55 Combine like terms: 55.235857919 + 55 = 110.235857919 x = 110.235857919 Simplifying x = 110.235857919Subproblem 2
x + -55 = -55.235857919 Simplifying x + -55 = -55.235857919 Reorder the terms: -55 + x = -55.235857919 Solving -55 + x = -55.235857919 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '55' to each side of the equation. -55 + 55 + x = -55.235857919 + 55 Combine like terms: -55 + 55 = 0 0 + x = -55.235857919 + 55 x = -55.235857919 + 55 Combine like terms: -55.235857919 + 55 = -0.235857919 x = -0.235857919 Simplifying x = -0.235857919Solution
The solution to the problem is based on the solutions from the subproblems. x = {110.235857919, -0.235857919}
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