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Simplifying x + 7 = 144x2 Reorder the terms: 7 + x = 144x2 Solving 7 + x = 144x2 Solving for variable 'x'. Combine like terms: 144x2 + -144x2 = 0 7 + x + -144x2 = 0 Begin completing the square. Divide all terms by -144 the coefficient of the squared term: Divide each side by '-144'. -0.04861111111 + -0.006944444444x + x2 = 0 Move the constant term to the right: Add '0.04861111111' to each side of the equation. -0.04861111111 + -0.006944444444x + 0.04861111111 + x2 = 0 + 0.04861111111 Reorder the terms: -0.04861111111 + 0.04861111111 + -0.006944444444x + x2 = 0 + 0.04861111111 Combine like terms: -0.04861111111 + 0.04861111111 = 0.00000000000 0.00000000000 + -0.006944444444x + x2 = 0 + 0.04861111111 -0.006944444444x + x2 = 0 + 0.04861111111 Combine like terms: 0 + 0.04861111111 = 0.04861111111 -0.006944444444x + x2 = 0.04861111111 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -0.006944444444x + 0.25 + x2 = 0.04861111111 + 0.25 Reorder the terms: 0.25 + -0.006944444444x + x2 = 0.04861111111 + 0.25 Combine like terms: 0.04861111111 + 0.25 = 0.29861111111 0.25 + -0.006944444444x + x2 = 0.29861111111 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.29861111111 Calculate the square root of the right side: 0.54645321 Break this problem into two subproblems by setting (x + 0.5) equal to 0.54645321 and -0.54645321.Subproblem 1
x + 0.5 = 0.54645321 Simplifying x + 0.5 = 0.54645321 Reorder the terms: 0.5 + x = 0.54645321 Solving 0.5 + x = 0.54645321 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 0.54645321 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.54645321 + -0.5 x = 0.54645321 + -0.5 Combine like terms: 0.54645321 + -0.5 = 0.04645321 x = 0.04645321 Simplifying x = 0.04645321Subproblem 2
x + 0.5 = -0.54645321 Simplifying x + 0.5 = -0.54645321 Reorder the terms: 0.5 + x = -0.54645321 Solving 0.5 + x = -0.54645321 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -0.54645321 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.54645321 + -0.5 x = -0.54645321 + -0.5 Combine like terms: -0.54645321 + -0.5 = -1.04645321 x = -1.04645321 Simplifying x = -1.04645321Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.04645321, -1.04645321}
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