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Simplifying 0.5x2 + -10x + 47 = 0 Reorder the terms: 47 + -10x + 0.5x2 = 0 Solving 47 + -10x + 0.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. 94 + -20x + x2 = 0 Move the constant term to the right: Add '-94' to each side of the equation. 94 + -20x + -94 + x2 = 0 + -94 Reorder the terms: 94 + -94 + -20x + x2 = 0 + -94 Combine like terms: 94 + -94 = 0 0 + -20x + x2 = 0 + -94 -20x + x2 = 0 + -94 Combine like terms: 0 + -94 = -94 -20x + x2 = -94 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 = -94 + 100 Reorder the terms: 100 + -20x + x2 = -94 + 100 Combine like terms: -94 + 100 = 6 100 + -20x + x2 = 6 Factor a perfect square on the left side: (x + -10)(x + -10) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (x + -10) equal to 2.449489743 and -2.449489743.Subproblem 1
x + -10 = 2.449489743 Simplifying x + -10 = 2.449489743 Reorder the terms: -10 + x = 2.449489743 Solving -10 + x = 2.449489743 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 = 2.449489743 + 10 Combine like terms: -10 + 10 = 0 0 + x = 2.449489743 + 10 x = 2.449489743 + 10 Combine like terms: 2.449489743 + 10 = 12.449489743 x = 12.449489743 Simplifying x = 12.449489743Subproblem 2
x + -10 = -2.449489743 Simplifying x + -10 = -2.449489743 Reorder the terms: -10 + x = -2.449489743 Solving -10 + x = -2.449489743 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 = -2.449489743 + 10 Combine like terms: -10 + 10 = 0 0 + x = -2.449489743 + 10 x = -2.449489743 + 10 Combine like terms: -2.449489743 + 10 = 7.550510257 x = 7.550510257 Simplifying x = 7.550510257Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.449489743, 7.550510257}
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