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Simplifying 900 + 4x = 109x2 Solving 900 + 4x = 109x2 Solving for variable 'x'. Combine like terms: 109x2 + -109x2 = 0 900 + 4x + -109x2 = 0 Begin completing the square. Divide all terms by -109 the coefficient of the squared term: Divide each side by '-109'. -8.256880734 + -0.03669724771x + x2 = 0 Move the constant term to the right: Add '8.256880734' to each side of the equation. -8.256880734 + -0.03669724771x + 8.256880734 + x2 = 0 + 8.256880734 Reorder the terms: -8.256880734 + 8.256880734 + -0.03669724771x + x2 = 0 + 8.256880734 Combine like terms: -8.256880734 + 8.256880734 = 0.000000000 0.000000000 + -0.03669724771x + x2 = 0 + 8.256880734 -0.03669724771x + x2 = 0 + 8.256880734 Combine like terms: 0 + 8.256880734 = 8.256880734 -0.03669724771x + x2 = 8.256880734 The x term is -0.03669724771x. Take half its coefficient (-0.01834862386). Square it (0.0003366719976) and add it to both sides. Add '0.0003366719976' to each side of the equation. -0.03669724771x + 0.0003366719976 + x2 = 8.256880734 + 0.0003366719976 Reorder the terms: 0.0003366719976 + -0.03669724771x + x2 = 8.256880734 + 0.0003366719976 Combine like terms: 8.256880734 + 0.0003366719976 = 8.2572174059976 0.0003366719976 + -0.03669724771x + x2 = 8.2572174059976 Factor a perfect square on the left side: (x + -0.01834862386)(x + -0.01834862386) = 8.2572174059976 Calculate the square root of the right side: 2.873537438 Break this problem into two subproblems by setting (x + -0.01834862386) equal to 2.873537438 and -2.873537438.Subproblem 1
x + -0.01834862386 = 2.873537438 Simplifying x + -0.01834862386 = 2.873537438 Reorder the terms: -0.01834862386 + x = 2.873537438 Solving -0.01834862386 + x = 2.873537438 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.01834862386' to each side of the equation. -0.01834862386 + 0.01834862386 + x = 2.873537438 + 0.01834862386 Combine like terms: -0.01834862386 + 0.01834862386 = 0.00000000000 0.00000000000 + x = 2.873537438 + 0.01834862386 x = 2.873537438 + 0.01834862386 Combine like terms: 2.873537438 + 0.01834862386 = 2.89188606186 x = 2.89188606186 Simplifying x = 2.89188606186Subproblem 2
x + -0.01834862386 = -2.873537438 Simplifying x + -0.01834862386 = -2.873537438 Reorder the terms: -0.01834862386 + x = -2.873537438 Solving -0.01834862386 + x = -2.873537438 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.01834862386' to each side of the equation. -0.01834862386 + 0.01834862386 + x = -2.873537438 + 0.01834862386 Combine like terms: -0.01834862386 + 0.01834862386 = 0.00000000000 0.00000000000 + x = -2.873537438 + 0.01834862386 x = -2.873537438 + 0.01834862386 Combine like terms: -2.873537438 + 0.01834862386 = -2.85518881414 x = -2.85518881414 Simplifying x = -2.85518881414Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.89188606186, -2.85518881414}
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