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Simplifying -4x2 + -5 + 7x + 15x2 + -14x = 0 Reorder the terms: -5 + 7x + -14x + -4x2 + 15x2 = 0 Combine like terms: 7x + -14x = -7x -5 + -7x + -4x2 + 15x2 = 0 Combine like terms: -4x2 + 15x2 = 11x2 -5 + -7x + 11x2 = 0 Solving -5 + -7x + 11x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -0.4545454545 + -0.6363636364x + x2 = 0 Move the constant term to the right: Add '0.4545454545' to each side of the equation. -0.4545454545 + -0.6363636364x + 0.4545454545 + x2 = 0 + 0.4545454545 Reorder the terms: -0.4545454545 + 0.4545454545 + -0.6363636364x + x2 = 0 + 0.4545454545 Combine like terms: -0.4545454545 + 0.4545454545 = 0.0000000000 0.0000000000 + -0.6363636364x + x2 = 0 + 0.4545454545 -0.6363636364x + x2 = 0 + 0.4545454545 Combine like terms: 0 + 0.4545454545 = 0.4545454545 -0.6363636364x + x2 = 0.4545454545 The x term is -0.6363636364x. Take half its coefficient (-0.3181818182). Square it (0.1012396694) and add it to both sides. Add '0.1012396694' to each side of the equation. -0.6363636364x + 0.1012396694 + x2 = 0.4545454545 + 0.1012396694 Reorder the terms: 0.1012396694 + -0.6363636364x + x2 = 0.4545454545 + 0.1012396694 Combine like terms: 0.4545454545 + 0.1012396694 = 0.5557851239 0.1012396694 + -0.6363636364x + x2 = 0.5557851239 Factor a perfect square on the left side: (x + -0.3181818182)(x + -0.3181818182) = 0.5557851239 Calculate the square root of the right side: 0.745509976 Break this problem into two subproblems by setting (x + -0.3181818182) equal to 0.745509976 and -0.745509976.Subproblem 1
x + -0.3181818182 = 0.745509976 Simplifying x + -0.3181818182 = 0.745509976 Reorder the terms: -0.3181818182 + x = 0.745509976 Solving -0.3181818182 + x = 0.745509976 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3181818182' to each side of the equation. -0.3181818182 + 0.3181818182 + x = 0.745509976 + 0.3181818182 Combine like terms: -0.3181818182 + 0.3181818182 = 0.0000000000 0.0000000000 + x = 0.745509976 + 0.3181818182 x = 0.745509976 + 0.3181818182 Combine like terms: 0.745509976 + 0.3181818182 = 1.0636917942 x = 1.0636917942 Simplifying x = 1.0636917942Subproblem 2
x + -0.3181818182 = -0.745509976 Simplifying x + -0.3181818182 = -0.745509976 Reorder the terms: -0.3181818182 + x = -0.745509976 Solving -0.3181818182 + x = -0.745509976 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3181818182' to each side of the equation. -0.3181818182 + 0.3181818182 + x = -0.745509976 + 0.3181818182 Combine like terms: -0.3181818182 + 0.3181818182 = 0.0000000000 0.0000000000 + x = -0.745509976 + 0.3181818182 x = -0.745509976 + 0.3181818182 Combine like terms: -0.745509976 + 0.3181818182 = -0.4273281578 x = -0.4273281578 Simplifying x = -0.4273281578Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0636917942, -0.4273281578}
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