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Simplifying 17x2 + 21x + -28 = 0 Reorder the terms: -28 + 21x + 17x2 = 0 Solving -28 + 21x + 17x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 17 the coefficient of the squared term: Divide each side by '17'. -1.647058824 + 1.235294118x + x2 = 0 Move the constant term to the right: Add '1.647058824' to each side of the equation. -1.647058824 + 1.235294118x + 1.647058824 + x2 = 0 + 1.647058824 Reorder the terms: -1.647058824 + 1.647058824 + 1.235294118x + x2 = 0 + 1.647058824 Combine like terms: -1.647058824 + 1.647058824 = 0.000000000 0.000000000 + 1.235294118x + x2 = 0 + 1.647058824 1.235294118x + x2 = 0 + 1.647058824 Combine like terms: 0 + 1.647058824 = 1.647058824 1.235294118x + x2 = 1.647058824 The x term is 1.235294118x. Take half its coefficient (0.617647059). Square it (0.3814878895) and add it to both sides. Add '0.3814878895' to each side of the equation. 1.235294118x + 0.3814878895 + x2 = 1.647058824 + 0.3814878895 Reorder the terms: 0.3814878895 + 1.235294118x + x2 = 1.647058824 + 0.3814878895 Combine like terms: 1.647058824 + 0.3814878895 = 2.0285467135 0.3814878895 + 1.235294118x + x2 = 2.0285467135 Factor a perfect square on the left side: (x + 0.617647059)(x + 0.617647059) = 2.0285467135 Calculate the square root of the right side: 1.42427059 Break this problem into two subproblems by setting (x + 0.617647059) equal to 1.42427059 and -1.42427059.Subproblem 1
x + 0.617647059 = 1.42427059 Simplifying x + 0.617647059 = 1.42427059 Reorder the terms: 0.617647059 + x = 1.42427059 Solving 0.617647059 + x = 1.42427059 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.617647059' to each side of the equation. 0.617647059 + -0.617647059 + x = 1.42427059 + -0.617647059 Combine like terms: 0.617647059 + -0.617647059 = 0.000000000 0.000000000 + x = 1.42427059 + -0.617647059 x = 1.42427059 + -0.617647059 Combine like terms: 1.42427059 + -0.617647059 = 0.806623531 x = 0.806623531 Simplifying x = 0.806623531Subproblem 2
x + 0.617647059 = -1.42427059 Simplifying x + 0.617647059 = -1.42427059 Reorder the terms: 0.617647059 + x = -1.42427059 Solving 0.617647059 + x = -1.42427059 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.617647059' to each side of the equation. 0.617647059 + -0.617647059 + x = -1.42427059 + -0.617647059 Combine like terms: 0.617647059 + -0.617647059 = 0.000000000 0.000000000 + x = -1.42427059 + -0.617647059 x = -1.42427059 + -0.617647059 Combine like terms: -1.42427059 + -0.617647059 = -2.041917649 x = -2.041917649 Simplifying x = -2.041917649Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.806623531, -2.041917649}
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