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Simplifying 3x2 + -45x + 70 = 0 Reorder the terms: 70 + -45x + 3x2 = 0 Solving 70 + -45x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 23.33333333 + -15x + x2 = 0 Move the constant term to the right: Add '-23.33333333' to each side of the equation. 23.33333333 + -15x + -23.33333333 + x2 = 0 + -23.33333333 Reorder the terms: 23.33333333 + -23.33333333 + -15x + x2 = 0 + -23.33333333 Combine like terms: 23.33333333 + -23.33333333 = 0.00000000 0.00000000 + -15x + x2 = 0 + -23.33333333 -15x + x2 = 0 + -23.33333333 Combine like terms: 0 + -23.33333333 = -23.33333333 -15x + x2 = -23.33333333 The x term is -15x. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15x + 56.25 + x2 = -23.33333333 + 56.25 Reorder the terms: 56.25 + -15x + x2 = -23.33333333 + 56.25 Combine like terms: -23.33333333 + 56.25 = 32.91666667 56.25 + -15x + x2 = 32.91666667 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 32.91666667 Calculate the square root of the right side: 5.737304826 Break this problem into two subproblems by setting (x + -7.5) equal to 5.737304826 and -5.737304826.Subproblem 1
x + -7.5 = 5.737304826 Simplifying x + -7.5 = 5.737304826 Reorder the terms: -7.5 + x = 5.737304826 Solving -7.5 + x = 5.737304826 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = 5.737304826 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 5.737304826 + 7.5 x = 5.737304826 + 7.5 Combine like terms: 5.737304826 + 7.5 = 13.237304826 x = 13.237304826 Simplifying x = 13.237304826Subproblem 2
x + -7.5 = -5.737304826 Simplifying x + -7.5 = -5.737304826 Reorder the terms: -7.5 + x = -5.737304826 Solving -7.5 + x = -5.737304826 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = -5.737304826 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -5.737304826 + 7.5 x = -5.737304826 + 7.5 Combine like terms: -5.737304826 + 7.5 = 1.762695174 x = 1.762695174 Simplifying x = 1.762695174Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.237304826, 1.762695174}
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