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Simplifying -7x2 + 8x + 10 + 2x2 + 6x + [-5] = 0 -7x2 + 8x + 10 + 2x2 + 6x + -5 = 0 Reorder the terms: 10 + -5 + 8x + 6x + -7x2 + 2x2 = 0 Combine like terms: 10 + -5 = 5 5 + 8x + 6x + -7x2 + 2x2 = 0 Combine like terms: 8x + 6x = 14x 5 + 14x + -7x2 + 2x2 = 0 Combine like terms: -7x2 + 2x2 = -5x2 5 + 14x + -5x2 = 0 Solving 5 + 14x + -5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -1 + -2.8x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -2.8x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -2.8x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2.8x + x2 = 0 + 1 -2.8x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -2.8x + x2 = 1 The x term is -2.8x. Take half its coefficient (-1.4). Square it (1.96) and add it to both sides. Add '1.96' to each side of the equation. -2.8x + 1.96 + x2 = 1 + 1.96 Reorder the terms: 1.96 + -2.8x + x2 = 1 + 1.96 Combine like terms: 1 + 1.96 = 2.96 1.96 + -2.8x + x2 = 2.96 Factor a perfect square on the left side: (x + -1.4)(x + -1.4) = 2.96 Calculate the square root of the right side: 1.720465053 Break this problem into two subproblems by setting (x + -1.4) equal to 1.720465053 and -1.720465053.Subproblem 1
x + -1.4 = 1.720465053 Simplifying x + -1.4 = 1.720465053 Reorder the terms: -1.4 + x = 1.720465053 Solving -1.4 + x = 1.720465053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.4' to each side of the equation. -1.4 + 1.4 + x = 1.720465053 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + x = 1.720465053 + 1.4 x = 1.720465053 + 1.4 Combine like terms: 1.720465053 + 1.4 = 3.120465053 x = 3.120465053 Simplifying x = 3.120465053Subproblem 2
x + -1.4 = -1.720465053 Simplifying x + -1.4 = -1.720465053 Reorder the terms: -1.4 + x = -1.720465053 Solving -1.4 + x = -1.720465053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.4' to each side of the equation. -1.4 + 1.4 + x = -1.720465053 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + x = -1.720465053 + 1.4 x = -1.720465053 + 1.4 Combine like terms: -1.720465053 + 1.4 = -0.320465053 x = -0.320465053 Simplifying x = -0.320465053Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.120465053, -0.320465053}
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