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Simplifying 0.3x2 + -42x + 1040 = 0 Reorder the terms: 1040 + -42x + 0.3x2 = 0 Solving 1040 + -42x + 0.3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.3 the coefficient of the squared term: Divide each side by '0.3'. 3466.666667 + -140x + x2 = 0 Move the constant term to the right: Add '-3466.666667' to each side of the equation. 3466.666667 + -140x + -3466.666667 + x2 = 0 + -3466.666667 Reorder the terms: 3466.666667 + -3466.666667 + -140x + x2 = 0 + -3466.666667 Combine like terms: 3466.666667 + -3466.666667 = 0.000000 0.000000 + -140x + x2 = 0 + -3466.666667 -140x + x2 = 0 + -3466.666667 Combine like terms: 0 + -3466.666667 = -3466.666667 -140x + x2 = -3466.666667 The x term is -140x. Take half its coefficient (-70). Square it (4900) and add it to both sides. Add '4900' to each side of the equation. -140x + 4900 + x2 = -3466.666667 + 4900 Reorder the terms: 4900 + -140x + x2 = -3466.666667 + 4900 Combine like terms: -3466.666667 + 4900 = 1433.333333 4900 + -140x + x2 = 1433.333333 Factor a perfect square on the left side: (x + -70)(x + -70) = 1433.333333 Calculate the square root of the right side: 37.859388968 Break this problem into two subproblems by setting (x + -70) equal to 37.859388968 and -37.859388968.Subproblem 1
x + -70 = 37.859388968 Simplifying x + -70 = 37.859388968 Reorder the terms: -70 + x = 37.859388968 Solving -70 + x = 37.859388968 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '70' to each side of the equation. -70 + 70 + x = 37.859388968 + 70 Combine like terms: -70 + 70 = 0 0 + x = 37.859388968 + 70 x = 37.859388968 + 70 Combine like terms: 37.859388968 + 70 = 107.859388968 x = 107.859388968 Simplifying x = 107.859388968Subproblem 2
x + -70 = -37.859388968 Simplifying x + -70 = -37.859388968 Reorder the terms: -70 + x = -37.859388968 Solving -70 + x = -37.859388968 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '70' to each side of the equation. -70 + 70 + x = -37.859388968 + 70 Combine like terms: -70 + 70 = 0 0 + x = -37.859388968 + 70 x = -37.859388968 + 70 Combine like terms: -37.859388968 + 70 = 32.140611032 x = 32.140611032 Simplifying x = 32.140611032Solution
The solution to the problem is based on the solutions from the subproblems. x = {107.859388968, 32.140611032}
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