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Simplifying x2 + 20x + 100 = 7 Reorder the terms: 100 + 20x + x2 = 7 Solving 100 + 20x + x2 = 7 Solving for variable 'x'. Reorder the terms: 100 + -7 + 20x + x2 = 7 + -7 Combine like terms: 100 + -7 = 93 93 + 20x + x2 = 7 + -7 Combine like terms: 7 + -7 = 0 93 + 20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-93' to each side of the equation. 93 + 20x + -93 + x2 = 0 + -93 Reorder the terms: 93 + -93 + 20x + x2 = 0 + -93 Combine like terms: 93 + -93 = 0 0 + 20x + x2 = 0 + -93 20x + x2 = 0 + -93 Combine like terms: 0 + -93 = -93 20x + x2 = -93 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 = -93 + 100 Reorder the terms: 100 + 20x + x2 = -93 + 100 Combine like terms: -93 + 100 = 7 100 + 20x + x2 = 7 Factor a perfect square on the left side: (x + 10)(x + 10) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (x + 10) equal to 2.645751311 and -2.645751311.Subproblem 1
x + 10 = 2.645751311 Simplifying x + 10 = 2.645751311 Reorder the terms: 10 + x = 2.645751311 Solving 10 + x = 2.645751311 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 = 2.645751311 + -10 Combine like terms: 10 + -10 = 0 0 + x = 2.645751311 + -10 x = 2.645751311 + -10 Combine like terms: 2.645751311 + -10 = -7.354248689 x = -7.354248689 Simplifying x = -7.354248689Subproblem 2
x + 10 = -2.645751311 Simplifying x + 10 = -2.645751311 Reorder the terms: 10 + x = -2.645751311 Solving 10 + x = -2.645751311 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 = -2.645751311 + -10 Combine like terms: 10 + -10 = 0 0 + x = -2.645751311 + -10 x = -2.645751311 + -10 Combine like terms: -2.645751311 + -10 = -12.645751311 x = -12.645751311 Simplifying x = -12.645751311Solution
The solution to the problem is based on the solutions from the subproblems. x = {-7.354248689, -12.645751311}
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