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Simplifying 1 = -10x2 + 13x + 3 Reorder the terms: 1 = 3 + 13x + -10x2 Solving 1 = 3 + 13x + -10x2 Solving for variable 'x'. Combine like terms: 1 + -3 = -2 -2 + -13x + 10x2 = 3 + 13x + -10x2 + -3 + -13x + 10x2 Reorder the terms: -2 + -13x + 10x2 = 3 + -3 + 13x + -13x + -10x2 + 10x2 Combine like terms: 3 + -3 = 0 -2 + -13x + 10x2 = 0 + 13x + -13x + -10x2 + 10x2 -2 + -13x + 10x2 = 13x + -13x + -10x2 + 10x2 Combine like terms: 13x + -13x = 0 -2 + -13x + 10x2 = 0 + -10x2 + 10x2 -2 + -13x + 10x2 = -10x2 + 10x2 Combine like terms: -10x2 + 10x2 = 0 -2 + -13x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.2 + -1.3x + x2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + -1.3x + 0.2 + x2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + -1.3x + x2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + -1.3x + x2 = 0 + 0.2 -1.3x + x2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 -1.3x + x2 = 0.2 The x term is -1.3x. Take half its coefficient (-0.65). Square it (0.4225) and add it to both sides. Add '0.4225' to each side of the equation. -1.3x + 0.4225 + x2 = 0.2 + 0.4225 Reorder the terms: 0.4225 + -1.3x + x2 = 0.2 + 0.4225 Combine like terms: 0.2 + 0.4225 = 0.6225 0.4225 + -1.3x + x2 = 0.6225 Factor a perfect square on the left side: (x + -0.65)(x + -0.65) = 0.6225 Calculate the square root of the right side: 0.788986692 Break this problem into two subproblems by setting (x + -0.65) equal to 0.788986692 and -0.788986692.Subproblem 1
x + -0.65 = 0.788986692 Simplifying x + -0.65 = 0.788986692 Reorder the terms: -0.65 + x = 0.788986692 Solving -0.65 + x = 0.788986692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.65' to each side of the equation. -0.65 + 0.65 + x = 0.788986692 + 0.65 Combine like terms: -0.65 + 0.65 = 0.00 0.00 + x = 0.788986692 + 0.65 x = 0.788986692 + 0.65 Combine like terms: 0.788986692 + 0.65 = 1.438986692 x = 1.438986692 Simplifying x = 1.438986692Subproblem 2
x + -0.65 = -0.788986692 Simplifying x + -0.65 = -0.788986692 Reorder the terms: -0.65 + x = -0.788986692 Solving -0.65 + x = -0.788986692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.65' to each side of the equation. -0.65 + 0.65 + x = -0.788986692 + 0.65 Combine like terms: -0.65 + 0.65 = 0.00 0.00 + x = -0.788986692 + 0.65 x = -0.788986692 + 0.65 Combine like terms: -0.788986692 + 0.65 = -0.138986692 x = -0.138986692 Simplifying x = -0.138986692Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.438986692, -0.138986692}
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