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Simplifying 4x2 + 4x = 69 Reorder the terms: 4x + 4x2 = 69 Solving 4x + 4x2 = 69 Solving for variable 'x'. Reorder the terms: -69 + 4x + 4x2 = 69 + -69 Combine like terms: 69 + -69 = 0 -69 + 4x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -17.25 + x + x2 = 0 Move the constant term to the right: Add '17.25' to each side of the equation. -17.25 + x + 17.25 + x2 = 0 + 17.25 Reorder the terms: -17.25 + 17.25 + x + x2 = 0 + 17.25 Combine like terms: -17.25 + 17.25 = 0.00 0.00 + x + x2 = 0 + 17.25 x + x2 = 0 + 17.25 Combine like terms: 0 + 17.25 = 17.25 x + x2 = 17.25 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. + 0.25 + x2 = 17.25 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 17.25 + 0.25 Combine like terms: 17.25 + 0.25 = 17.5 1.25 + x2 = 17.5 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 17.5 Calculate the square root of the right side: 4.183300133 Break this problem into two subproblems by setting (x + 0.5) equal to 4.183300133 and -4.183300133.Subproblem 1
x + 0.5 = 4.183300133 Simplifying x + 0.5 = 4.183300133 Reorder the terms: 0.5 + x = 4.183300133 Solving 0.5 + x = 4.183300133 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 = 4.183300133 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 4.183300133 + -0.5 x = 4.183300133 + -0.5 Combine like terms: 4.183300133 + -0.5 = 3.683300133 x = 3.683300133 Simplifying x = 3.683300133Subproblem 2
x + 0.5 = -4.183300133 Simplifying x + 0.5 = -4.183300133 Reorder the terms: 0.5 + x = -4.183300133 Solving 0.5 + x = -4.183300133 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 = -4.183300133 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -4.183300133 + -0.5 x = -4.183300133 + -0.5 Combine like terms: -4.183300133 + -0.5 = -4.683300133 x = -4.683300133 Simplifying x = -4.683300133Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.683300133, -4.683300133}
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