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Simplifying 100x2 = x + (x + 15) Reorder the terms: 100x2 = x + (15 + x) Remove parenthesis around (15 + x) 100x2 = x + 15 + x Reorder the terms: 100x2 = 15 + x + x Combine like terms: x + x = 2x 100x2 = 15 + 2x Solving 100x2 = 15 + 2x Solving for variable 'x'. Reorder the terms: -15 + -2x + 100x2 = 15 + 2x + -15 + -2x Reorder the terms: -15 + -2x + 100x2 = 15 + -15 + 2x + -2x Combine like terms: 15 + -15 = 0 -15 + -2x + 100x2 = 0 + 2x + -2x -15 + -2x + 100x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -15 + -2x + 100x2 = 0 Begin completing the square. Divide all terms by 100 the coefficient of the squared term: Divide each side by '100'. -0.15 + -0.02x + x2 = 0 Move the constant term to the right: Add '0.15' to each side of the equation. -0.15 + -0.02x + 0.15 + x2 = 0 + 0.15 Reorder the terms: -0.15 + 0.15 + -0.02x + x2 = 0 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + -0.02x + x2 = 0 + 0.15 -0.02x + x2 = 0 + 0.15 Combine like terms: 0 + 0.15 = 0.15 -0.02x + x2 = 0.15 The x term is -0.02x. Take half its coefficient (-0.01). Square it (0.0001) and add it to both sides. Add '0.0001' to each side of the equation. -0.02x + 0.0001 + x2 = 0.15 + 0.0001 Reorder the terms: 0.0001 + -0.02x + x2 = 0.15 + 0.0001 Combine like terms: 0.15 + 0.0001 = 0.1501 0.0001 + -0.02x + x2 = 0.1501 Factor a perfect square on the left side: (x + -0.01)(x + -0.01) = 0.1501 Calculate the square root of the right side: 0.387427413 Break this problem into two subproblems by setting (x + -0.01) equal to 0.387427413 and -0.387427413.Subproblem 1
x + -0.01 = 0.387427413 Simplifying x + -0.01 = 0.387427413 Reorder the terms: -0.01 + x = 0.387427413 Solving -0.01 + x = 0.387427413 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.01' to each side of the equation. -0.01 + 0.01 + x = 0.387427413 + 0.01 Combine like terms: -0.01 + 0.01 = 0.00 0.00 + x = 0.387427413 + 0.01 x = 0.387427413 + 0.01 Combine like terms: 0.387427413 + 0.01 = 0.397427413 x = 0.397427413 Simplifying x = 0.397427413Subproblem 2
x + -0.01 = -0.387427413 Simplifying x + -0.01 = -0.387427413 Reorder the terms: -0.01 + x = -0.387427413 Solving -0.01 + x = -0.387427413 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.01' to each side of the equation. -0.01 + 0.01 + x = -0.387427413 + 0.01 Combine like terms: -0.01 + 0.01 = 0.00 0.00 + x = -0.387427413 + 0.01 x = -0.387427413 + 0.01 Combine like terms: -0.387427413 + 0.01 = -0.377427413 x = -0.377427413 Simplifying x = -0.377427413Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.397427413, -0.377427413}
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