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Simplifying x2 + 30 = 42x + 23 Reorder the terms: 30 + x2 = 42x + 23 Reorder the terms: 30 + x2 = 23 + 42x Solving 30 + x2 = 23 + 42x Solving for variable 'x'. Reorder the terms: 30 + -23 + -42x + x2 = 23 + 42x + -23 + -42x Combine like terms: 30 + -23 = 7 7 + -42x + x2 = 23 + 42x + -23 + -42x Reorder the terms: 7 + -42x + x2 = 23 + -23 + 42x + -42x Combine like terms: 23 + -23 = 0 7 + -42x + x2 = 0 + 42x + -42x 7 + -42x + x2 = 42x + -42x Combine like terms: 42x + -42x = 0 7 + -42x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-7' to each side of the equation. 7 + -42x + -7 + x2 = 0 + -7 Reorder the terms: 7 + -7 + -42x + x2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -42x + x2 = 0 + -7 -42x + x2 = 0 + -7 Combine like terms: 0 + -7 = -7 -42x + x2 = -7 The x term is -42x. Take half its coefficient (-21). Square it (441) and add it to both sides. Add '441' to each side of the equation. -42x + 441 + x2 = -7 + 441 Reorder the terms: 441 + -42x + x2 = -7 + 441 Combine like terms: -7 + 441 = 434 441 + -42x + x2 = 434 Factor a perfect square on the left side: (x + -21)(x + -21) = 434 Calculate the square root of the right side: 20.832666656 Break this problem into two subproblems by setting (x + -21) equal to 20.832666656 and -20.832666656.Subproblem 1
x + -21 = 20.832666656 Simplifying x + -21 = 20.832666656 Reorder the terms: -21 + x = 20.832666656 Solving -21 + x = 20.832666656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '21' to each side of the equation. -21 + 21 + x = 20.832666656 + 21 Combine like terms: -21 + 21 = 0 0 + x = 20.832666656 + 21 x = 20.832666656 + 21 Combine like terms: 20.832666656 + 21 = 41.832666656 x = 41.832666656 Simplifying x = 41.832666656Subproblem 2
x + -21 = -20.832666656 Simplifying x + -21 = -20.832666656 Reorder the terms: -21 + x = -20.832666656 Solving -21 + x = -20.832666656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '21' to each side of the equation. -21 + 21 + x = -20.832666656 + 21 Combine like terms: -21 + 21 = 0 0 + x = -20.832666656 + 21 x = -20.832666656 + 21 Combine like terms: -20.832666656 + 21 = 0.167333344 x = 0.167333344 Simplifying x = 0.167333344Solution
The solution to the problem is based on the solutions from the subproblems. x = {41.832666656, 0.167333344}
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