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Simplifying 16(3.14) = 3.14(x2 + -20x + 100) Multiply 16 * 3.14 50.24 = 3.14(x2 + -20x + 100) Reorder the terms: 50.24 = 3.14(100 + -20x + x2) 50.24 = (100 * 3.14 + -20x * 3.14 + x2 * 3.14) 50.24 = (314 + -62.8x + 3.14x2) Solving 50.24 = 314 + -62.8x + 3.14x2 Solving for variable 'x'. Combine like terms: 50.24 + -314 = -263.76 -263.76 + 62.8x + -3.14x2 = 314 + -62.8x + 3.14x2 + -314 + 62.8x + -3.14x2 Reorder the terms: -263.76 + 62.8x + -3.14x2 = 314 + -314 + -62.8x + 62.8x + 3.14x2 + -3.14x2 Combine like terms: 314 + -314 = 0 -263.76 + 62.8x + -3.14x2 = 0 + -62.8x + 62.8x + 3.14x2 + -3.14x2 -263.76 + 62.8x + -3.14x2 = -62.8x + 62.8x + 3.14x2 + -3.14x2 Combine like terms: -62.8x + 62.8x = 0.0 -263.76 + 62.8x + -3.14x2 = 0.0 + 3.14x2 + -3.14x2 -263.76 + 62.8x + -3.14x2 = 3.14x2 + -3.14x2 Combine like terms: 3.14x2 + -3.14x2 = 0.00 -263.76 + 62.8x + -3.14x2 = 0.00 Begin completing the square. Divide all terms by -3.14 the coefficient of the squared term: Divide each side by '-3.14'. 84 + -20x + x2 = 0 Move the constant term to the right: Add '-84' to each side of the equation. 84 + -20x + -84 + x2 = 0 + -84 Reorder the terms: 84 + -84 + -20x + x2 = 0 + -84 Combine like terms: 84 + -84 = 0 0 + -20x + x2 = 0 + -84 -20x + x2 = 0 + -84 Combine like terms: 0 + -84 = -84 -20x + x2 = -84 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = -84 + 100 Reorder the terms: 100 + -20x + x2 = -84 + 100 Combine like terms: -84 + 100 = 16 100 + -20x + x2 = 16 Factor a perfect square on the left side: (x + -10)(x + -10) = 16 Calculate the square root of the right side: 4 Break this problem into two subproblems by setting (x + -10) equal to 4 and -4.Subproblem 1
x + -10 = 4 Simplifying x + -10 = 4 Reorder the terms: -10 + x = 4 Solving -10 + x = 4 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 4 + 10 Combine like terms: -10 + 10 = 0 0 + x = 4 + 10 x = 4 + 10 Combine like terms: 4 + 10 = 14 x = 14 Simplifying x = 14Subproblem 2
x + -10 = -4 Simplifying x + -10 = -4 Reorder the terms: -10 + x = -4 Solving -10 + x = -4 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -4 + 10 Combine like terms: -10 + 10 = 0 0 + x = -4 + 10 x = -4 + 10 Combine like terms: -4 + 10 = 6 x = 6 Simplifying x = 6Solution
The solution to the problem is based on the solutions from the subproblems. x = {14, 6}
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