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Simplifying 5x2 + 11x = -3 Reorder the terms: 11x + 5x2 = -3 Solving 11x + 5x2 = -3 Solving for variable 'x'. Reorder the terms: 3 + 11x + 5x2 = -3 + 3 Combine like terms: -3 + 3 = 0 3 + 11x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.6 + 2.2x + x2 = 0 Move the constant term to the right: Add '-0.6' to each side of the equation. 0.6 + 2.2x + -0.6 + x2 = 0 + -0.6 Reorder the terms: 0.6 + -0.6 + 2.2x + x2 = 0 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + 2.2x + x2 = 0 + -0.6 2.2x + x2 = 0 + -0.6 Combine like terms: 0 + -0.6 = -0.6 2.2x + x2 = -0.6 The x term is 2.2x. Take half its coefficient (1.1). Square it (1.21) and add it to both sides. Add '1.21' to each side of the equation. 2.2x + 1.21 + x2 = -0.6 + 1.21 Reorder the terms: 1.21 + 2.2x + x2 = -0.6 + 1.21 Combine like terms: -0.6 + 1.21 = 0.61 1.21 + 2.2x + x2 = 0.61 Factor a perfect square on the left side: (x + 1.1)(x + 1.1) = 0.61 Calculate the square root of the right side: 0.781024968 Break this problem into two subproblems by setting (x + 1.1) equal to 0.781024968 and -0.781024968.Subproblem 1
x + 1.1 = 0.781024968 Simplifying x + 1.1 = 0.781024968 Reorder the terms: 1.1 + x = 0.781024968 Solving 1.1 + x = 0.781024968 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.1' to each side of the equation. 1.1 + -1.1 + x = 0.781024968 + -1.1 Combine like terms: 1.1 + -1.1 = 0.0 0.0 + x = 0.781024968 + -1.1 x = 0.781024968 + -1.1 Combine like terms: 0.781024968 + -1.1 = -0.318975032 x = -0.318975032 Simplifying x = -0.318975032Subproblem 2
x + 1.1 = -0.781024968 Simplifying x + 1.1 = -0.781024968 Reorder the terms: 1.1 + x = -0.781024968 Solving 1.1 + x = -0.781024968 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.1' to each side of the equation. 1.1 + -1.1 + x = -0.781024968 + -1.1 Combine like terms: 1.1 + -1.1 = 0.0 0.0 + x = -0.781024968 + -1.1 x = -0.781024968 + -1.1 Combine like terms: -0.781024968 + -1.1 = -1.881024968 x = -1.881024968 Simplifying x = -1.881024968Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.318975032, -1.881024968}
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