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Simplifying 4x2 + x + 10 = 100 Reorder the terms: 10 + x + 4x2 = 100 Solving 10 + x + 4x2 = 100 Solving for variable 'x'. Reorder the terms: 10 + -100 + x + 4x2 = 100 + -100 Combine like terms: 10 + -100 = -90 -90 + x + 4x2 = 100 + -100 Combine like terms: 100 + -100 = 0 -90 + x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -22.5 + 0.25x + x2 = 0 Move the constant term to the right: Add '22.5' to each side of the equation. -22.5 + 0.25x + 22.5 + x2 = 0 + 22.5 Reorder the terms: -22.5 + 22.5 + 0.25x + x2 = 0 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + 0.25x + x2 = 0 + 22.5 0.25x + x2 = 0 + 22.5 Combine like terms: 0 + 22.5 = 22.5 0.25x + x2 = 22.5 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. 0.25x + 0.25 + x2 = 22.5 + 0.25 Reorder the terms: 0.25 + 0.25x + x2 = 22.5 + 0.25 Combine like terms: 22.5 + 0.25 = 22.75 0.25 + 0.25x + x2 = 22.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 22.75 Calculate the square root of the right side: 4.769696007 Break this problem into two subproblems by setting (x + 0.5) equal to 4.769696007 and -4.769696007.Subproblem 1
x + 0.5 = 4.769696007 Simplifying x + 0.5 = 4.769696007 Reorder the terms: 0.5 + x = 4.769696007 Solving 0.5 + x = 4.769696007 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 = 4.769696007 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 4.769696007 + -0.5 x = 4.769696007 + -0.5 Combine like terms: 4.769696007 + -0.5 = 4.269696007 x = 4.269696007 Simplifying x = 4.269696007Subproblem 2
x + 0.5 = -4.769696007 Simplifying x + 0.5 = -4.769696007 Reorder the terms: 0.5 + x = -4.769696007 Solving 0.5 + x = -4.769696007 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 = -4.769696007 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -4.769696007 + -0.5 x = -4.769696007 + -0.5 Combine like terms: -4.769696007 + -0.5 = -5.269696007 x = -5.269696007 Simplifying x = -5.269696007Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.269696007, -5.269696007}
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